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The number of ways, in which 12 identical coins can be put int

Question

The number of ways, in which 12 identical coins can be put into 5 different purses, if none of the purses remain empty, is

660

110

165

330

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The number of ways, in which 12 identical coins can be put into 5 different purses, if none of the purses remain empty, is

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Text solutionVerified

Coefficient of

x^{12}

(x^{1} + x^{2} + x^{3} + x^{4} + x^{5} + ...)^{5}

=

coefficient of

x^{7}

(1 + x + x^{2} + x^{3} + ...)^{5}

=

coefficient of

x^{7}

(1 - x)^{- 5}

= 1 +^{5} C_{1} x +^{6} C_{2} x^{2} + ... +^{11} C_{7} x^{7}

=

coefficient of

^{11} C_{7} = \frac{11.10.9.8}{4.3.2.1} = 11 \times 30 = 330

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Question Text	The number of ways, in which 12 identical coins can be put into 5 different purses, if none of the purses remain empty, is
Answer Type	Text solution:1
Upvotes	150