# Q. How many five-digit prime numbers can be obtained by using all the digits 1, 2, 3, 4 and 5 without repetition of digits?

(a) Zero

(b) One

(c) Nine

(d) Ten

Correct Answer: (a) Zero

#### Question from UPSC Prelims 2020 CSAT Paper

**Explanation : **

## Five-digit prime numbers

To determine how many five-digit prime numbers can be obtained by using all the digits 1, 2, 3, 4, and 5 without repetition, we can use the fact that a number is prime if and only if it is divisible only by 1 and itself.

Next, consider the sum of the digits of any five-digit number formed using these digits. The sum is 1 + 2 + 3 + 4 + 5 = 15, which is divisible by 3. Therefore, Zero is the answer.