In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, Benjamin, Charlene must be on the line before each of Frederick, Gale, and Elaine?
Options:
(A) 1,008
(B) 1,296
(C) 1,512
(D) 2*1008
(E) 2,268 Stream of consciousness:
Place D and H first: 8 options for D, 7 options for H
We are left with 6 empty places. A, B and C must take first 3 places and F, G, Emust take the remaining three. A, B and C can be arranged in their places in 3! ways. The same for F, G, and E
Total = 8*7*3!*3! = 2*1008
Thus, the answer is (D).