Question

A company has 5 senior executives and 8 junior executives. If a committee of 3 executives is formed at random, what is the probability that all 3 are senior executives?

Select one:

a. 3/56

b. 3/13

c. 1/56

d. 5/143

Answer 1

The probability that all 3 executives are senior executives is 5/143

Step-by-step explanation:

To find the probability that all 3 executives are senior executives, we need to calculate the probability of selecting 3 senior executives from a total of 13 executives.

The total number of ways to choose 3 executives from 13 is given by the combination formula ;

C(13, 3) = 286.

The number of ways to choose 3 senior executives from 5 is given by the combination formula;

C(5, 3) = 10.

So, the probability that all 3 executives are senior executives is ;

10/286 = 5/143.