Problema Solution
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
orders
(b) all the bands of each type must perform in a row
orders
Answer provided by our tutors
These are permutations because the order does matter and because the bands are distinguishable from each other.
(a)
You have 5 + 2 = 7 bands to play. We assume that the bands are distinguishable (in other words, even if two bands are both country music bands, it matters what order they play in.)
7 bands (not considering any restrictions) can play in 7! ways.
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040 orders
(b)
There are two possible orders:
1) All the 5 country music bands first, then the 2 rock bands --> 5! x 2! = 120 x 2 = 240 orders
2) All the 2 rock bands first, then the 5 country music bands --> 3! x 5! = 2 x 120 = 240 orders
So the total number of orders would be 2*240 = 480.