JEE Main 2024 (Online) 5th April Morning ShiftQuestion 1
The number of ways of getting a sum $16$ on throwing a dice four times is $\_\_\_\_\_\_\_\_$ .
Permutation and Combination
Answer$125$
Solution
Coefficient of $x^{16}$ in $(x+\ldots+x^6)^4$, i.e. of $x^{12}$ in $\left(\frac{1-x^6}{1-x}\right)^4$: $\binom{15}3-4\binom93+6\binom33=455-336+6=125$.