Question

An experiment involves 16 participants. From these, a group of 4 participants is to be tested under a special condition. How many groups of 4 participants can be chosen, assuming that the order in which the participants are chosen is irrelevant? (If necessary consult a list of formulas.)

Answer 1

43,680 ways.

Explanation:

We have been given that an experiment involves 16 participants. From these, a group of 4 participants is to be tested under a special condition. We are asked to find the number of groups of 4 participants that can be chosen, assuming that the order in which the participants are chosen is irrelevant.

We will use permutations formula to solve our given problem.

`^nP_r=(n!)/((n-r)!)`

For our given problem
`n=16` and
`r=4`.

`^(16)P_4=(16!)/((16-4)!)`

`^(16)P_4=(16!)/(12!)=(16*15*14*13*12!)/(12!)=16*15*14*13=43,680`

Therefore, 4 participants can be chosen in 43,680 different ways.