The number of ways of getting a sum 16 on throwing a dice four times is ________.

Question

The number of ways of getting a sum 16 on throwing a dice four times is \_\_\_\_\_\_\_\_.

Answer: 125

Accepted Answer

Number of ways $=$ coefficient of ${x}^{16}$ in $(x+{x}^{2}+\ldots +$ ${{x}^{6})}^{4}$

$=$ coefficient of ${x}^{16}$ in ${(1-{x}^{6})}^{4}(1-x{)}^{-4}$

$=$ coefficient of ${x}^{16}$ in $(1-4{x}^{6}+6{x}^{12}\ldots )(1-x{)}^{-4}$

$={}^{15}{C}_{3}-4\cdot {}^{9}{C}_{3}+6=125$

Solutions · 1