Question

4. Seven of ten employees of a Corporation are men. Suppose that 4 employees are selected at random as delegates for a conference. How many selections will contain: a) exactly 3 men? b) at least3 men? c) what is the probability that a random selection will contain exactly 3 men?

Answer 1

(a)

Number of men = 7

Number of women = 4

Total employees = 11

Number of employees selected = 4

Number of ways of selecting 3 men from 7 men =

$inom{7}{3}=rac{7!}{4!(7-3)!}=35$

Number of ways of selecting 1 woman from 4 women = 4

So,

Exactly 3 men = 35 X 4 = 140

(b)

Number of men = 7

Number of women = 4

Total employees = 11

Number of employees selected = 4

Number of ways of selecting 3 men from 7 men =

$inom{7}{3}=rac{7!}{4!(7-3)!}=35$

Number of ways of selecting 1 woman from 4 women = 4

So,

Exactly 3 men = 35 X 4 = 140

Number of ways of selecting 4 men from 7 men =

So,

Exactly 4 men = 35

So,

at least 3 men = 140 + 35 = 175

(c)

Number of men = 7

Number of women = 4

Total employees = 11

Number of employees selected = 4

Number of ways of selecting 4 employees from 11 employees =

Number of ways of selecting 3 men from 7 men =

$inom{7}{3}=rac{7!}{4!(7-3)!}=35$

Number of ways of selecting 1 woman from 4 women = 4

So,

Exactly 3 men = 35 X 4 = 140

So,

Probability of exactly 3 men = 140/330 = 0.4242