Permutations & Combinations
Permutation and Combination
star_batch_jee_advanced_2025
Grade 11
Question:
Let $p = 2520$, $x = $ number of divisors of $p$ which are multiples of 6, $y = $ number of divisors of $p$ which are multiples of 9, then:
x = 24
x = 12
y = 16
y = 12
Step-by-Step Solution
Key Concept: Complex binomial coefficient equations often reduce to simple polynomial equations after expanding and collecting like terms.
From $\binom{m}{2}x^n \binom{2}{n}\binom{1}{-m} \binom{1}{-n} \binom{1}{m} = -m$, we simplify to $(m-n)^2 + 3(m-n) = 0$, factoring as $(m-n)(m-n+3) = 0$. This gives $n - m = 3$ (since $m-n=0$ leads to contradiction).
Correct Answer: 1,3