The number of ways in which 17 apples can be distributed among four guests such that each guest gets at…
The number of ways in which 17 apples can be distributed among four guests such that each guest gets at least 3 apples is
1140
336
36
56
Solution
Required number of ways $=$ Coeff. of $x^{17}$ in $\left(x^3+x^4 \ldots\right)^4$
$=\text { Coeff. of } x^5 \text { in }\left(1+x+x^2 \ldots\right)^4$ Coeff. of $x^5$ in $(1-x)^{-4}={ }^8 \mathrm{C}_5=\frac{8 \times 7 \times 6}{3 \times 2 \times 1}=56$