If n! and (n + 1)! have the same units digit, then n can be which of the following?
I. n = 10
II. n = 1
III. n = 0  Choose the correct option:
A) I only	B) II only	C) III only	D) I and III	E) I, II, and III
Given: n! and (n + 1)! have the same units digits   Let us first write down the factorials of different numbers:   0! = 1   1! = 1   2! = 2   3! = 6   4! = 24   5! = 120   6! = 720   If we notice here, all the numbers after 4! will end with a 0.   Here is why:   If we multiply any number by 10, a 0 is added to that number   And a 10 is formed by a 5 and a 2, 10 = 5*2   Till 4!, we do not have a "5" in multiplication. But after that, we will have atleast one "5" in the multiplication.   Hence the units digits will be same after 5! and for 0! and 1!   Now checking the statements   I. n = 10   Yes, the units digits of 10! and 11! are same and = 0. TRUE   II. n = 1   units digit f 1! = 1 and units digit of 2! = 2. FALSE   III. n = 0   Units digit of 1! = 1 and units digit of 0! = 1. TRUE   Correct Option: I and III
<result>D</result>
If n! and (n + 1)! have the same units digit, then n can be which of the following?
I. n = 10
II. n = 1
III. n = 0