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

2 Answers
Aug 8, 2016

Answer:

#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#

Aug 8, 2016

Answer:

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#