fabiobf wrote:

A folk group wants to have one concert on each of the seven consecutive nights starting January 1 of next year. One concert is to be held in each of cities A, B, C, D and E. Two concerts are to be held in city F, but not on consecutive nights. In how many ways can the group decide on the venues for these seven concerts?

(A) 10 x 5!

(B) 14 x 5!

(C) 15 x 5!

(D) 20 x 5!

(E) 21 x 5!

The folk group can have the concerts in the following ways

_A_B_C_D_E_

City F can take any of 6 places as two concerts can't be held on consecutive nights.

Since there are 6 spots where the concerts can take place in City F,

we have 6c2 or 15 different ways of arranging these concerts.

Also, the concerts in the other 5 cities(A,B,C,D and E) can be arranged in 5! ways

Hence, the total number of ways in which the folk group can decide on its venues for each

of the seven concerts is

15*5!(Option C)
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