Question

Answer the questions below. (a) From the 12 albums released by a musician, the recording company wishes to release 9 in a boxed set. How many different boxed sets are possible? (b) An experiment involves 31 participants. From these, a group of 5 participants is to be tested under a special condition. How many groups of 5 participants are possible?

Answer 1

a) Number of ways to select 9 albums from 12 albums is computed here as:

$= \binom{12}{9} = \frac{12!}{9!(12 - 9)!} = 220$

therefore 220 boxed sets are possible here.

b) The number of ways to select  5 participants from 31 participants here is computed here as:

$= \binom{31}{5} = \frac{31!}{5!(31 - 5)!} = 169911$

Therefore there are 169,911 combinations are possible here.