Five persons are selected from a group of 8 men, 6 women and 6 children. Find the probability that 3 of the 5 persons selected are children.

 To find the probability that 3 of the 5 persons selected are children, we need to determine the total number of ways of selecting 5 people from the group of 8 men, 6 women, and 6 children and the number of ways of selecting 3 children from the 6 children.

The total number of ways of selecting 5 people from a group of 20 people is given by the combination formula:

C(20,5) = 20! / (5! * 15!) = 15504

The number of ways of selecting 3 children from a group of 6 children is given by the combination formula:

C(6,3) = 6! / (3! * 3!) = 20

The number of ways of selecting the remaining 2 people from the group of 14 adults (8 men and 6 women) is given by the combination formula:

C(14,2) = 14! / (2! * 12!) = 91

Therefore, the total number of ways of selecting 5 people with 3 children is:

20 * 91 = 1820

The probability of selecting 3 children from a group of 5 people is:

1820 / 15504 ≈ 0.1175

So, the probability that 3 of the 5 persons selected are children is approximately 0.1175 or 11.75%.