The letters A, B, C, D and E are arranged in such a way that there are exactly two letters between A and E.…
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?
12
18
24
36
Solution
With exactly two letters between A and E, the (A,E) pair gives 4 placement patterns (A__E_, _A__E, E__A_, _E__A). The three remaining blanks are filled by B, C, D in $3! = 6$ ways. Total = $4 \times 6 = 24$.