Step-by-step 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...
