TS EAMCET · Maths · Permutation Combination
The number of ways in which 15 identical gold coins can be distributed among 3 persons such that each one gets atleast 3 gold coins is
- A 27
- B 28
- C 22
- D 25
Answer & Solution
Correct Answer
(B) 28
Step-by-step Solution
Detailed explanation
Let \(x_1, x_2, x_3\) be the no. of coins received by 3 persons. \(x_1 \geq 3, x_2 \geq 3, x_3 \geq 3\) No. of ways of distribution is Coefficient of \(x^{15}\) in \(\left(x^3+x^4+x^5+x^6 \ldots\right)^3\) \(=\) Coefficient of \(x^6\) in \((1-x)^{-3}={ }^8 C_6=28\).
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