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

Aug 8, 2016

$210 \div 2 = 105$

#### 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 $15 \times 14$ 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.

$\frac{210}{2} = 105$

Aug 8, 2016

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

$= 105$