Solving Generating Function when there is condition on two variables.












2












$begingroup$


" Find the number of ways of giving 10 identical gift boxes to 6 people : A, B, C, D, E, F in such a way that total number of boxes given to A and B together does not exceed 4. "



I tried it in this way :



[$x^{10}$] $(1+x^{1}+...+x^{4})^{2}*( 1+x^{2}+....)^{4}$



But I am not sure if its right or not , can anyone help me with the condition on A and B i.e say $x_1+x_2leq 4$






generating-functions







share|cite|improve this question











$endgroup$

















    2












    $begingroup$


    " Find the number of ways of giving 10 identical gift boxes to 6 people : A, B, C, D, E, F in such a way that total number of boxes given to A and B together does not exceed 4. "



    I tried it in this way :



    [$x^{10}$] $(1+x^{1}+...+x^{4})^{2}*( 1+x^{2}+....)^{4}$



    But I am not sure if its right or not , can anyone help me with the condition on A and B i.e say $x_1+x_2leq 4$






    generating-functions







    share|cite|improve this question











    $endgroup$















      2












      2








      2





      $begingroup$


      " Find the number of ways of giving 10 identical gift boxes to 6 people : A, B, C, D, E, F in such a way that total number of boxes given to A and B together does not exceed 4. "



      I tried it in this way :



      [$x^{10}$] $(1+x^{1}+...+x^{4})^{2}*( 1+x^{2}+....)^{4}$



      But I am not sure if its right or not , can anyone help me with the condition on A and B i.e say $x_1+x_2leq 4$






      generating-functions







      share|cite|improve this question











      $endgroup$




      " Find the number of ways of giving 10 identical gift boxes to 6 people : A, B, C, D, E, F in such a way that total number of boxes given to A and B together does not exceed 4. "



      I tried it in this way :



      [$x^{10}$] $(1+x^{1}+...+x^{4})^{2}*( 1+x^{2}+....)^{4}$



      But I am not sure if its right or not , can anyone help me with the condition on A and B i.e say $x_1+x_2leq 4$






      generating-functions




      generating-functions






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Dec 22 '18 at 12:52







      CHETAN RAJPUT

















      asked Dec 22 '18 at 12:40









      CHETAN RAJPUTCHETAN RAJPUT

      205




      205






















          1 Answer
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          2












          $begingroup$

          What you've to find is $x_1+x_2+x_3+x_4+x_5+x_6=10$ (I've replaced A-F by 1-6). Further, $x_igeq 0$ and $x_1+x_2leq 4$.



          Required answer= $$sum_{i=0}^{4}(Coeff. of x^i in (x^0+x^1+cdots x^4)cdot (x^0+x^1+cdots x^4))cdot(Coeff. of x^{10-i} in (x^0+x^1+cdots x^{10})^4)$$
          Can you solve it now?




          In open form, it can also be written as:
          $$(Coeff. of x^0 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{10} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^1 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{9} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^2 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{8} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^3 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{7} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^4 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{6} in (x^0+x^1+cdots x^{10})^4)$$






          share|cite|improve this answer











          $endgroup$









          • 2




            $begingroup$
            Okay. I got that. I haven't came across this case so I am not fully getting it. I ll cross check the answer then analyse it. Thanx
            $endgroup$
            – CHETAN RAJPUT
            Dec 22 '18 at 13:25






          • 1




            $begingroup$
            issuu.com/imsf/docs/mcs-033/25 It has unit 2, generating functions
            $endgroup$
            – Ankit Kumar
            Dec 22 '18 at 13:37








          • 2




            $begingroup$
            Thank you for sharing it. I got 2121 , check if its fine.
            $endgroup$
            – CHETAN RAJPUT
            Dec 22 '18 at 15:03








          • 1




            $begingroup$
            Thanx. answer is correct.
            $endgroup$
            – CHETAN RAJPUT
            Dec 22 '18 at 16:39






          • 1




            $begingroup$
            @CHETANRAJPUT you're welcome
            $endgroup$
            – Ankit Kumar
            Dec 22 '18 at 16:52











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          2












          $begingroup$

          What you've to find is $x_1+x_2+x_3+x_4+x_5+x_6=10$ (I've replaced A-F by 1-6). Further, $x_igeq 0$ and $x_1+x_2leq 4$.



          Required answer= $$sum_{i=0}^{4}(Coeff. of x^i in (x^0+x^1+cdots x^4)cdot (x^0+x^1+cdots x^4))cdot(Coeff. of x^{10-i} in (x^0+x^1+cdots x^{10})^4)$$
          Can you solve it now?




          In open form, it can also be written as:
          $$(Coeff. of x^0 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{10} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^1 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{9} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^2 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{8} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^3 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{7} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^4 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{6} in (x^0+x^1+cdots x^{10})^4)$$






          share|cite|improve this answer











          $endgroup$









          • 2




            $begingroup$
            Okay. I got that. I haven't came across this case so I am not fully getting it. I ll cross check the answer then analyse it. Thanx
            $endgroup$
            – CHETAN RAJPUT
            Dec 22 '18 at 13:25






          • 1




            $begingroup$
            issuu.com/imsf/docs/mcs-033/25 It has unit 2, generating functions
            $endgroup$
            – Ankit Kumar
            Dec 22 '18 at 13:37








          • 2




            $begingroup$
            Thank you for sharing it. I got 2121 , check if its fine.
            $endgroup$
            – CHETAN RAJPUT
            Dec 22 '18 at 15:03








          • 1




            $begingroup$
            Thanx. answer is correct.
            $endgroup$
            – CHETAN RAJPUT
            Dec 22 '18 at 16:39






          • 1




            $begingroup$
            @CHETANRAJPUT you're welcome
            $endgroup$
            – Ankit Kumar
            Dec 22 '18 at 16:52
















          2












          $begingroup$

          What you've to find is $x_1+x_2+x_3+x_4+x_5+x_6=10$ (I've replaced A-F by 1-6). Further, $x_igeq 0$ and $x_1+x_2leq 4$.



          Required answer= $$sum_{i=0}^{4}(Coeff. of x^i in (x^0+x^1+cdots x^4)cdot (x^0+x^1+cdots x^4))cdot(Coeff. of x^{10-i} in (x^0+x^1+cdots x^{10})^4)$$
          Can you solve it now?




          In open form, it can also be written as:
          $$(Coeff. of x^0 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{10} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^1 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{9} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^2 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{8} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^3 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{7} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^4 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{6} in (x^0+x^1+cdots x^{10})^4)$$






          share|cite|improve this answer











          $endgroup$









          • 2




            $begingroup$
            Okay. I got that. I haven't came across this case so I am not fully getting it. I ll cross check the answer then analyse it. Thanx
            $endgroup$
            – CHETAN RAJPUT
            Dec 22 '18 at 13:25






          • 1




            $begingroup$
            issuu.com/imsf/docs/mcs-033/25 It has unit 2, generating functions
            $endgroup$
            – Ankit Kumar
            Dec 22 '18 at 13:37








          • 2




            $begingroup$
            Thank you for sharing it. I got 2121 , check if its fine.
            $endgroup$
            – CHETAN RAJPUT
            Dec 22 '18 at 15:03








          • 1




            $begingroup$
            Thanx. answer is correct.
            $endgroup$
            – CHETAN RAJPUT
            Dec 22 '18 at 16:39






          • 1




            $begingroup$
            @CHETANRAJPUT you're welcome
            $endgroup$
            – Ankit Kumar
            Dec 22 '18 at 16:52














          2












          2








          2





          $begingroup$

          What you've to find is $x_1+x_2+x_3+x_4+x_5+x_6=10$ (I've replaced A-F by 1-6). Further, $x_igeq 0$ and $x_1+x_2leq 4$.



          Required answer= $$sum_{i=0}^{4}(Coeff. of x^i in (x^0+x^1+cdots x^4)cdot (x^0+x^1+cdots x^4))cdot(Coeff. of x^{10-i} in (x^0+x^1+cdots x^{10})^4)$$
          Can you solve it now?




          In open form, it can also be written as:
          $$(Coeff. of x^0 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{10} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^1 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{9} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^2 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{8} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^3 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{7} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^4 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{6} in (x^0+x^1+cdots x^{10})^4)$$






          share|cite|improve this answer











          $endgroup$



          What you've to find is $x_1+x_2+x_3+x_4+x_5+x_6=10$ (I've replaced A-F by 1-6). Further, $x_igeq 0$ and $x_1+x_2leq 4$.



          Required answer= $$sum_{i=0}^{4}(Coeff. of x^i in (x^0+x^1+cdots x^4)cdot (x^0+x^1+cdots x^4))cdot(Coeff. of x^{10-i} in (x^0+x^1+cdots x^{10})^4)$$
          Can you solve it now?




          In open form, it can also be written as:
          $$(Coeff. of x^0 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{10} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^1 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{9} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^2 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{8} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^3 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{7} in (x^0+x^1+cdots x^{10})^4)$$$$+(Coeff. of x^4 in (x^0+x^1+cdots x^4)^2)cdot(Coeff. of x^{6} in (x^0+x^1+cdots x^{10})^4)$$







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited Dec 22 '18 at 13:18

























          answered Dec 22 '18 at 12:58









          Ankit KumarAnkit Kumar

          1,514221




          1,514221








          • 2




            $begingroup$
            Okay. I got that. I haven't came across this case so I am not fully getting it. I ll cross check the answer then analyse it. Thanx
            $endgroup$
            – CHETAN RAJPUT
            Dec 22 '18 at 13:25






          • 1




            $begingroup$
            issuu.com/imsf/docs/mcs-033/25 It has unit 2, generating functions
            $endgroup$
            – Ankit Kumar
            Dec 22 '18 at 13:37








          • 2




            $begingroup$
            Thank you for sharing it. I got 2121 , check if its fine.
            $endgroup$
            – CHETAN RAJPUT
            Dec 22 '18 at 15:03








          • 1




            $begingroup$
            Thanx. answer is correct.
            $endgroup$
            – CHETAN RAJPUT
            Dec 22 '18 at 16:39






          • 1




            $begingroup$
            @CHETANRAJPUT you're welcome
            $endgroup$
            – Ankit Kumar
            Dec 22 '18 at 16:52














          • 2




            $begingroup$
            Okay. I got that. I haven't came across this case so I am not fully getting it. I ll cross check the answer then analyse it. Thanx
            $endgroup$
            – CHETAN RAJPUT
            Dec 22 '18 at 13:25






          • 1




            $begingroup$
            issuu.com/imsf/docs/mcs-033/25 It has unit 2, generating functions
            $endgroup$
            – Ankit Kumar
            Dec 22 '18 at 13:37








          • 2




            $begingroup$
            Thank you for sharing it. I got 2121 , check if its fine.
            $endgroup$
            – CHETAN RAJPUT
            Dec 22 '18 at 15:03








          • 1




            $begingroup$
            Thanx. answer is correct.
            $endgroup$
            – CHETAN RAJPUT
            Dec 22 '18 at 16:39






          • 1




            $begingroup$
            @CHETANRAJPUT you're welcome
            $endgroup$
            – Ankit Kumar
            Dec 22 '18 at 16:52








          2




          2




          $begingroup$
          Okay. I got that. I haven't came across this case so I am not fully getting it. I ll cross check the answer then analyse it. Thanx
          $endgroup$
          – CHETAN RAJPUT
          Dec 22 '18 at 13:25




          $begingroup$
          Okay. I got that. I haven't came across this case so I am not fully getting it. I ll cross check the answer then analyse it. Thanx
          $endgroup$
          – CHETAN RAJPUT
          Dec 22 '18 at 13:25




          1




          1




          $begingroup$
          issuu.com/imsf/docs/mcs-033/25 It has unit 2, generating functions
          $endgroup$
          – Ankit Kumar
          Dec 22 '18 at 13:37






          $begingroup$
          issuu.com/imsf/docs/mcs-033/25 It has unit 2, generating functions
          $endgroup$
          – Ankit Kumar
          Dec 22 '18 at 13:37






          2




          2




          $begingroup$
          Thank you for sharing it. I got 2121 , check if its fine.
          $endgroup$
          – CHETAN RAJPUT
          Dec 22 '18 at 15:03






          $begingroup$
          Thank you for sharing it. I got 2121 , check if its fine.
          $endgroup$
          – CHETAN RAJPUT
          Dec 22 '18 at 15:03






          1




          1




          $begingroup$
          Thanx. answer is correct.
          $endgroup$
          – CHETAN RAJPUT
          Dec 22 '18 at 16:39




          $begingroup$
          Thanx. answer is correct.
          $endgroup$
          – CHETAN RAJPUT
          Dec 22 '18 at 16:39




          1




          1




          $begingroup$
          @CHETANRAJPUT you're welcome
          $endgroup$
          – Ankit Kumar
          Dec 22 '18 at 16:52




          $begingroup$
          @CHETANRAJPUT you're welcome
          $endgroup$
          – Ankit Kumar
          Dec 22 '18 at 16:52


















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