InterviewSolution
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InterviewSolution
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In how many different ways can 3 persons A, B, C having 6 one-rupeecoin 7 one-rupee coin, 8 one-rupee coin, respectively, donate 10 one-rupee coin collectively? |
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Answer» Let A, B and C donate `x_(1),x_(2),x_(3)` number of one-rupee coins. `therefore x_(1)+x_(2)+x_(3)=10`, where `0 le x_(1) le 6, 0 le x_(2) le 7, 0 le x_(3) le 8` ` therefore` Required number of ways =coefficient to `p^(10) " in " (1+p+p^(2)+..+p^(6))xx(1+p+p^(2)+..+p^(7))xx(1+p+p^(2)+..+p^(8))` (In each bracket series is not extended to infinite terms as upper limit of each variable is less than 10) =coefficient to `p^(10) " in " ((1-p^(7))/(1-p))((1-p^(8))/(1-p))((1-p^(9))/(1-p))` =coefficient of `p^(10) " in " (1-p^(7))(1-p^(8))(1-p^(9))(1-p)^(-3)` =coefficient of `p^(10) " in " (1-p^(7)-p^(8)-p^(9))xx(1+ ""^(3)C_(1)p+ ""^(4)C_(2)p^(2)+ ""^(5)C_(3)p^(3)+..+ ""^(12)C_(10)p^(10)+..)` `=""^(12)C_(10)- ""^(5)C_(3)- ""^(4)C_(2)- ""^(3)C_(1)` =66-10-6-3 =47 |
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