Question

A four-digit number is formed by using digits 1,2,3,4 without repetition. What is the probability that the number is divisible by 4?

• A. 1/4
• B. 1/2
• C. 3/5
• D. 4/5
• E. None of these

Answer 1

The correct option is A

1/4

A number divisible by 4 formed using the digits 1,2,3,4 has to have the last two digits as 12 or 24 or 32.
In each of these cases, the four digit number can be formed using the remaining 2 digits in 2! = 2 ways.

A number divisible by 4 can be formed in 3×2 = 6 ways.

Total no. of numbers that can be formed using the digits 1,2,3,4 without repetition
= 4! = 24

Required probability = $\frac{6}{24}$ = $\frac{1}{4}$.