Question

I need help with this please?
A parent-teacher committee consisting of 4 people is to be formed from 20 parents and 5 teachers. Find the probability that the committee will consist of these people:
a. All teachers
b. 2 teachers and 2 parents c. All parents
d. 1 teacher and 3 parents

Answer 1

a. since they choose 4 people to form the committee and all the people chosen are teachers
from 5 teacher, we choose 4, 5C4
and
from 20 parents, we choose none, 20C0
5C4*20C0= 5

b. from 5 teacher choose 2, 5C2
and
from 20 parents choose 2, 20C2

5C2 * 20C2=1900

c.all parents
from 5 teachers choose 0, 5C0
and
from 20 parents choose 4, 20C4

5C0 * 20C4= 4845

d. from 5 teacher choose 1, 5C1
and
from 20 parents choose 3, 20C3

5C1 * 20C3= 5700