Q57 / 160 · TS EAMCET 2024 (09 May Shift 1) · Mathematics
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
- A27
- Correct answerB28
- C22
- D25
Solution
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 $(1-x)^{-3}={ }^8 C_6=28$.
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 $(1-x)^{-3}={ }^8 C_6=28$.
Hence, the correct answer is option: 'B'.