(a)

A committee of four is selected from a total of 4 freshman, 5 sophomores, and 6 juniors.

Find the probability of the event that committee consisting atleast 3 freshman.

Atleast 3 freshman refers to committe can have 3 or 4 freshman.

Number of selections for committee having atleast 3 freshman is .

Number of combinations for committe having atleast 3 freshman is 45.

Probability

.

.

The probability that committe having atleast 3 freshman is 0.03. \ \

(b)

Find the probability that the committee consisting all four of them are of same class.

Number of ways of selecting a committee having all four of them from the same class is .

Probability.

The probability that committe having  all four of them are of same class is  0.015.

(c)

Find the probability that the committee consisting not all four of them are of same class.

Probability

From (b), probability that committe having  all four of them are of same class is  0.015.

Probability that committe having not all four of them are of same class is 0.985. \ \

(d)

Find the probability that the committee consisting exactly 3 of them are of same class.

Exactly 3 of them are of same class refers to only  3 are of same class and 1 from other class.

Number of selections for committee having exactly 3 of them are of same class is .

Probability

Probability that the committee consisting exactly 3 of them are of same class is 0.23. \ \