# Q. The letters A, B, C, D and E are arranged in such a way that there are exactly two letters between A and E. How many such arrangements are possible?

a. 12

b. 18

c.Β 24

d. 36

Correct Answer: c. 24

#### Question from UPSC Prelims 2022 CSAT Paper

**Explanation :Β **

## Letters A B C D and E are arranged

The problem asks for the number of arrangements of the letters A, B, C, D and E such that there are exactly two letters between A and E. There are four possible arrangements for A and E: A _ _ E _, _ A _ _ E, E _ _ A _, and _ E _ _ A. For each of these arrangements, there are 3! = 6 ways to arrange the remaining letters B, C and D. So the total number of arrangements is 4 * 6 = 24.