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28 Apr 2025, 07:40
Kudos
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samriddhi1234
The method shared by Bunuel above is pretty much it. I am elaborating the steps below if it helps you see it more clearly.
10! - 2*(5!)^2
10*9*8*7*6*5! - 2*5! * 5! (Writing 10! in terms of 5!)
5! (10*9*8*7*6 - 2*5!) (taking 5! common)
5! * (10*9*8*7*6 - 2*5*4*3*2*1)
5! * (10*9*8*7*6 - 10*4*6*1)
5! * 10 * 6 (504 - 4)
5! * 10 * 6 * 500
5*4! * (5*2) * 6 * (5 * 5*2 * 5*2)
This product has five 5s and enough 2s so it will end with 5 zeroes.
Answer (E)
If the last step is a problem, check this post: https://anaprep.com/number-properties-h ... actorials/
