This was confusing for me too, but the logic lies in the fact that 49! is a factorial. 1x2x3x4....40x41x...49. vs. 51 which is just 17x3. There are no 5s in 51. The formula allows you to count how many 5s are in factorials. If it was 51! (factorial) then yes it would have 12 fives, but the answer is 10 because 51 is NOT a factorial in this problem (after you simplify it.)
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