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JEE Main · 2024 · 05 Apr 2024 · Shift 1 · Permutations and Combinations

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

Answer: 125

Solution

Count solutions of

x_{1} + x_{2} + x_{3} + x_{4} = 16

with each

1 \leq x_{i} \leq 6

, i.e. the coefficient of

t^{16}

in

(t + t^{2} + \dots + t^{6})^{4} = t^{4} (\frac{1 - t ^{6}}{1 - t})^{4}

. Need the coefficient of

t^{12}

in

(1 - t^{6})^{4} (1 - t)^{- 4}

:

(3 15) - 4 (3 9) + 6 (3 3) = 455 - 336 + 6 = 125.

JEE Main · 2024 · 05 Apr 2024 · Shift 1 · Integer answer

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