# How many ways can you buy 2 DVDs from a

How many ways can you buy 2 DVDs from a display of 15?
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verrainellewtzri
Step 1
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 $15×14$ choices $=210$.
Step 2
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.
$\frac{210}{2}=105$
###### Not exactly what you’re looking for?
Jaime Coleman
Step 1
Assumption: choosing $a+b$ is classified the same as choosing $b+a$.
This is the condition of 'combinations'
Step 2
$⇒{.}^{n}{C}_{r}\to \frac{n!}{\left(n-r\right)!r!}$
$⇒{.}^{n}{C}_{r}\to {.}^{15}{C}_{2}\to \frac{15!}{\left(15-2\right)!2!}$
$=\frac{15×14×\overline{)13!}}{\overline{)13!}.2!}=\frac{15×14}{2}$
$=105$