Question

Assertion (A ): $\frac{(n + 3)!}{(n - 1)!} $ is divisible by $24 (n \in N)$.
Reason (R ): Product of any four consecutive integers is divisible by $4!$.

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A).
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true.

Answer 1

Answer: (A)

$\frac{(n + 3)!}{(n - 1)!} = \frac{(n + 3)(n + 2)(n + 1)n(n-1)!}{(n -1)!}$
$= n (n+ 1) (n + 2) (n + 3)$ is the product of four consecutive integers & it is divisible by $24$.