Statistics

Confusing Permutations and Combinations

Students use a permutation formula when they are only choosing a group, or use a combination formula when different orders should count separately.

Quick check

Why students make it

The word choose can make every counting problem feel the same. Students often count the same group many times because they do not first decide whether order matters.

The rule done right

Use permutations when order matters, such as arranging winners for 1st, 2nd, and 3rd place. Use combinations when order does not matter, with P(n,r)=n!(n−r)!P(n,r)=\frac{n!}{(n-r)!} and (nr)=n!r!(n−r)!\binom{n}{r}=\frac{n!}{r!(n-r)!}.

Related resources

countingpermutationscombinations