Question

Question #b9013

Answer 1

`"_14C_3 = 364`

Explanation:

This is a combination problem and can be written as

`14C3` or `"_14C_3`.

The formula for a combination is

`"_nC_r = (n!)/(r!(n-r)!`
(combinations of `r` objects taken from a total set of `n` objects)

`"_14C_3 = (14!)/(3!(14-3)!) = 364`.

Note that many calculators have this formula built in.

Also, this is a combination problem rather than a permutation because in combinations order does not matter. In other words, it doesn't matter which applicant is chosen first, second or third. If person A is chosen first, person B chosen second and person C chosen third, we can call this group ABC. This is the same group of three people as the groups chosen in the order ACB or BCA, etc.

If order DOES matter, it is a permutation problem (e.g. three people finishing 1st/2nd/3rd in a race).