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?

Correct Answer: (C) 24

There are 5 positions (1, 2, 3, 4, 5) to place letters A, B, C, D, and E. For exactly two letters to be between A and E, their occupied positions must be either $\{1, 4\}$ or $\{2, 5\}$ (2 possible position pairs). In each pair, A and E can be arranged in $2! = 2$ ways. The remaining 3 letters (B, C, D) can be arranged in the remaining 3 positions in $3! = 6$ ways. Therefore, the total number of possible arrangements is $2$$\times$ 2 $\times$ 6 = 24.