First slide

Permutations

Question

The tensdigit of 1! + 2! + 3! + … + 49! is

Moderate

A

1
B

2
C

3
D

4

Solution

We know that 1! + 2! + 3! + 4! = 33
Also, 5! = 120, 6! = 720, 7! = 5040, 8! = 40320 and 9! = 362880.
Thus, tens digit of 1! + 2! + … + 9! is 1.
Also, note that n! is divisible by 100 for all n ≥ 10. Therefore, the tens digit of 1! + 2! + … + 49! is 1.

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