Question

Do you know how to find the answer for b? Six 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 if the following conditions apply? A) there are no restrictions on the order. B) all bands of each type must perform in a row

Answer 1

There are 6 country music bands and 2 rock bands.

Total = 6+2 = 8 bands

A) there are no restrictions on the order.

When there are no restrictions then any of the music bands can play in any order.

The total number of ways is given by

$8!=40320$

So, there are 40320 ways

B) all bands of each type must perform in a row.

Now we have a restriction that all bands of each type (country and rock) must perform in a row.

So, there are two possibilities

6 country bands perform first then 2 rock bands

$6!\times2!=720\times2=1440$

Or 2 rock bands perform first then 6 country bands

$2!\times6!=2\times720=1440$

The total number of wats is given by

$1440+1440=2880$

So, there are 2880 ways