For some natural number n, assume that (15,000)! is divisible by (n!)!. The largest possible value of n is:
Explanation:
For (15,000)! to be completely divisible by (n!)!, n! ≤ 15,000
Now we know, 6! = 720 7! = 5,040 8! = 40,320
∵ n ≤ 15,000, highest value n can take is 7
Hence, option (c).
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