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Five country music bands and 2 rock bands are signed up to perform at an all-day festival.
How many different orders can the bands play in if the following conditions apply?
(a) there are no restrictions on the order
(b) all the bands of each type must perform in a row
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(a) (5 + 2)! = 7! = = 1*2*3*4*5*6*7 = 5040 different ways (permutations).
(b) 2 * 5! * 2! = 2 * (1*2*3*4*5) * (1*2) = 2 * 120 * 2 = 480 different ways.
Solved.