QUESTION

CSAT

Easy

Maths

Prelims 2022

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?

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Explanation

Condition Given: There are exactly two letters between A and E in the arrangement.
Possible Positions for A and E: Since there are two letters between A and E, A and E can either be in the following pairs of positions: A__E_ A__E E__A _E__A

There are 4 possible ways to place A and E while keeping exactly two letters between them.

Arrangements of Remaining Letters (B, C, D): The number of ways to arrange B, C, and D in 3 positions is $3! = 6$ .
Total Arrangements: For each of the 4 ways to place A and E, there are 6 ways to arrange B, C, and D. Total arrangements = $4 \times 6 = 24$ .