Math miscellaneousHard
Question
Number of possible values of n such that n! has exactly 20 zeroes at the end is equal to -
Options
A.4
B.5
C.6
D.7
Solution
Let number of zeroes = x = 
⇒ x <
(∵ [x] ≤ x)
⇒ x <
⇒ n > 80
If n = 80, x =
If n = 85, x =
If n = 90, x =
⇒ n ∈ {85, 86, 87, 88, 89}
⇒ x <
(∵ [x] ≤ x)⇒ x <
⇒ n > 80
If n = 80, x =
If n = 85, x =
If n = 90, x =
⇒ n ∈ {85, 86, 87, 88, 89}
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