Question

A four digit number is formed by using the digits 1,2,3,4,5,6,7 without repetition. What is the probability that it's divisible by 2?

• A. 4/7
• B. 1/7
• C. 2/7
• D. 3/7

Answer 1

The correct option is D

3/7

A four digit number out of the given digits can be formed by filling the first place by any of the 7 digits, second by any of the remaining 6 digits, third by any of the remaining 5 digits and last place by any of the remaining the 4 digits.i.e. in ⁷P₄ ways=840 ways.

To form an even number the unit's place can be filled up by any one of the digits 2, 4 or 6.i.e. in 3 ways. For the other places, we have respectively remaining 6, 5 and 4 digits left. So this job can be done in ⁶P₃ ways. So total number of ways =3 x (⁶P₃) =360.

So, the required probability=360/840=3/7.