QJEEM24Mae6a6: JEE Main 2024 Mathematics - Class 11 JEEM24Mae6a6 Solution: The number of ways of getting a sum 16 on throwing a dice four…

Question

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

Accepted Answer

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

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

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

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

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