Question

In the French Honor Society, there are 12 girls and 8 boys.

This summer, they are taking a trip to France and only 8
people can go. Find the probability that each of the
following groups will be randomly selected to go on the trip
to France.
a) All girls

b) All boys

c) 4 girls and 4 boys

d) 3 girls and 5 boys

e) At least one boy

f) At least two girls

Answer 1

a) All girls - 12C8 /20 C8

b) All boys - 8C8/20C8

c) 4 girls and 4 boys - 8C4 * 12C4/20 C8

d) 3 girls and 5 boys - 8C5 * 12C3/20 C8

e) At least one boy - 1 - 12C8 /20 C8

f) At least two girls 1 - (1 - 8C8 /20 C8)

Explanation:

Given -

Total girls - 12

Total boys - 8

a) All girls - 12C8 /20 C8

b) All boys - 8C8/20C8

c) 4 girls and 4 boys - 8C4 * 12C4/20 C8

d) 3 girls and 5 boys - 8C5 * 12C3/20 C8

e) At least one boy - 1 - 12C8 /20 C8

f) At least two girls 1 - (1 - 8C8 /20 C8)