Question

Decide if the following problem is an example of a permutation or a combination. State your rationale. For a study, 4 people are chosen at random from a group of 10 people. How many ways can this be done?

Answer 1

The correct answer would be a combination.

A combination is a way of selecting items from a collection/group. The order of selection does not matter. More specifically, combinations refer to the combination of a group of n people (10) taken k people (4) at a time without repetition.

n = 10
k = 4
C(n, k) = n! / (k! * (n−k)!) = 10! / (4! * (10 - 4)!) = 210

The correct result for the above example would be: 210 possible ways of choosing 4 people randomly from a group of 10 people.