The number of ways of getting a sum 16 on throwing a dice four times is ________.
Answer (integer)
125
Solution
<p>Number of ways $=$ coefficient of $x^{16}$ in $\left(x+x^2+\ldots+\right.$ $\left.x^6\right)^4$</p>
<p>$=$ coefficient of $x^{16}$ in $\left(1-x^6\right)^4(1-x)^{-4}$</p>
<p>$=$ coefficient of $x^{16}$ in $\left(1-4 x^6+6 x^{12} \ldots\right)(1-x)^{-4}$</p>
<p>$={ }^{15} C_3-4 \cdot{ }^9 C_3+6=125$</p>
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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