Question

An experiment involves 17 participants. From these, a group of 3 participants is to be tested under a special condition. How many groups of 3 participants can
be chosen, assuming that the order in which the participants are chosen is irrelevant?
​

Answer 1

Answer: 680

Step-by-step explanation:

When order doesn't matter,then the number of combinations of choosing r things out of n = $^nC_r=\dfrac{n!}{r!(n-r)!}$

Given: Total participants = 17

From these, a group of 3 participants is to be tested under a special condition.

Number of groups of 3 participants chosen = $^{17}C_3=\dfrac{17!}{3!(17-3)!}$

$^{17}C_3=\dfrac{17!}{3!(17-3)!}\\\\=\dfrac{17\times16\times15\times14!}{3\times2\times14!}\\\\=680$

Hence, there are 680 groups of 3 participants can  be chosen,.