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.
[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]
For our given problem [tex]n=16[/tex] and [tex]r=4[/tex].
[tex]^{16}P_4=\frac{16!}{(16-4)!}[/tex]
[tex]^{16}P_4=\frac{16!}{12!}=\frac{16*15*14*13*12!}{12!}=16*15*14*13=43,680[/tex]
Therefore, 4 participants can be chosen in 43,680 different ways.
