Tricky...
Let S be the set of non-negative integers less than 100. A number is chosen at random. What is the probability that the factorial of the number (n!) Has 1 or 2 digits?
The probability can be expressed as a/b for coprime integers a and b.
Find a+b
Details and assumptions
N!= N(N-1)(N-2).....3x2x1
The answer is 21.
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S = {0, 1, 2, ..., 99}
n(S) = 100
0! = 1
1! = 1
2! = 2
3! = 6
4! = 24
5/100 = 1/20
1 + 20 = 21