A committee consisting of 6 people is to be selected from eight parents and four teachers. find the probability of selecting three parents and three teachers.

All in all, there are 12 people including 8 parents and 4 teachers. To choose 6 out of this 12 people, we use the concept of combination.

n = 12C6 = 924

To choose, 3 parents out of the 8 parents, we use again the concept of combination.

x = 8C3 = 56

Similarly, we use the same concept for choosing 3 teachers out of 4 teachers.

y = 4C3 = 4

The probability required in this item can be solved through the equation,

P = xy/n

Substituting,

P = (56) (4) / 924 = 0.2424

Thus, the probability is 24.24%.