singhsa wrote:A television advertising break is to consist of six 30-second advertisements. If the second, fourth, and sixth of the 30-second spots are to be filled with three different advertisements for company X and the other spots are to be filled with one advertisement each for companies A, B, and C, in how many different ways can the six advertisements be ordered?
(A) 729
(B) 720
(C) 120
(D) 36
(E) 24
OA soon
Let's call the 6 spots X1, X2, X3, A, B and C.
Number of choices for spot 1 = 3 (A, B or C)
Number of choices for spot 2 = 3 (X1, X2, or X3)
Number of choices for spot 3 = 2 (2 remaining choices of A, B and C)
Number of choices for spot 4 = 2 (2 remaining choices of X1, X2 and X3)
Number of choices for spot 5 = 1 (1 remaining choice of A, B and C)
Number of choices for spot 6 = 1 (1 remaining choice of X1, X2 and X3)
To combine the number of choices for each spot, we multiply:
3*3*2*2*1*1 = 36.
The correct answer is
D.
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