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The number of ways in which 20 identical...

The number of ways in which `20` identical coins be distributed in `4` persons if each person receive at least `2` coins and atmost `5` coins, are

A

`.^(15)C_(12) - 4. .^(11)C_(8) + 6. .^(7)C_(4) - 4`

B

`.^(15)C_(3) - 6. . ^(11)C_(8) + .^(7)C_(4)`

C

`.^(23)C_(3)`

D

`.^(15)C_(0)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Number of ways `=` coefficient of `x^(20)` in
`(x^(2) + x^(3) + x^(4) + x^(5))^(4) = x^(B) (1 + x + x^(2) + x^(3))^(4)`
`=` coefficient of `x^(12)` in `((1 - x^(4))/(1 - x))^(4) = (1 - 4^(4))^(4)(1 - x)^(-4)`
`=.^(15)C_(12) - 4 . .^(11)C_(8) + 6. .^(7)(C_(4) - 4 = 1 = .^(15)C_(0)`
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