Question

How many ways can you buy 2 DVDs from a display of 15?

Answer 1

`210div 2 = 105`

Explanation:

We assume that someone will not buy two of the same DVD.

For the first DVD, there is a choice of 15 , but once the first is bought, there is a choice of 14 for the second one.

There are `15xx14` choices = `210`

However, this does not take order into consideration .... the 2 DVD's might be the same, just bought in a different order, so we need to divide this number by 2 to avoid the duplicates.

`210/2 = 105`

Answer 2

105

Explanation:

Assumption: choosing `a+b` is classified the same as choosing `b+a`

This is the condition of 'combinations'

`=> color(white)(.)^nC_r -> (n!)/((n-r)!r!)`

`=> color(white)(.)^nC_r -> color(white)(.)^15C_2->(15!)/((15-2)!2!)`

`=(15xx14xxcancel(13!))/(cancel(13!)color(white)(.)2!) =(15xx14)/2`

`=105`