Permutations & Combinations
Dice — Number of Ways to Get Sum 16
nta_pyq_2024_apr
Grade 11
Question:
The number of ways of getting a sum 16 on throwing a dice four times is
Step-by-Step Solution
Key Concept: Coefficient of $x^{16}$ in $(x+x^2+\cdots+x^6)^4=x^4\left(\frac{1-x^6}{1-x}\right)^4$. Find coefficient of $x^{12}$ in $(1-x^6)^4(1-x)^{-4}$.
$^{15}C_3-4\cdot^9C_6+6=455-336+6=125$.
Correct Answer: 125