For some natural number n, assume that (15,000)! is divisible by (n!)!. The largest possible value of n is
To find the largest possible value of n, we need to find the value of n such that n! is less than 15000.
7! = 5040
8! = 40320 > 15000
This implies 15000! is not divisible by 40320!
Therefore, maximum value n can take is 7.
The answer is option B.