Question

Among the contestants in a competition are 46 women and 23 men. If 5 winners are randomly selected, what is the probability that they are all men?

Answer 1

Answer:

When 5 winners are randomly selected, the probability that they are all men is 0.003.

Step-by-step explanation:

Among the contestants in a competition are 46 women and 23 men.

Total persons are =$46+23=69$

When one winner is chosen, there are 68 people left, when second winner is chosen there are 67 people left and so on.

So, the probability that they are all men is given by:

$\frac{23}{69} \times\frac{22}{68} \times\frac{21}{67} \times\frac{20}{66} \times\frac{19}{65}$

= $\frac{4037880}{1348621560}$ = 0.002999 ≈ 0.003

Therefore, when 5 winners are randomly selected, the probability that they are all men is 0.003.