Question

. There are seven people in a club: A, B, C, D, E, F, and G. A committee of 3 people is formed. What is the probability that G is on the committee

Answer 1

Explanation:

there are 7 over 4 total possibilities to create a group of 3 or if 7.

that is

7! / (4! × (7-4)!) = 7×6×5 / 3×2 = 7×5 = 35

for the probability we need also the number of the desired cases, a the probability is

number of desired cases / number of total cases

the desired cases are all combinations, where G is a part of.

for that we make G a constant, and now we have only 6 variable candidates for the other 2 positions on the committee.

that is 6 over 2 or

6! / (2! × (6-2)!) = 6×5/2 = 3×5 = 15

so, the probability that G is in the committee is

15/35 = 3/7 = 0.428571429...