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

Answer:

43,680 ways.

Step-by-step 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.

$^nP_r=\frac{n!}{(n-r)!}$

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

$^{16}P_4=\frac{16!}{(16-4)!}$

$^{16}P_4=\frac{16!}{12!}=\frac{16*15*14*13*12!}{12!}=16*15*14*13=43,680$

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