A group consists of 6 men and 5 women. five people are selected to attend a conference. in how many ways can 5 people be selected from this group of 11? in how many ways can 5 men be selected from the 6 men? find the probability that the selected group will consist of all men.

To compute for combinations, we will use the method nCr = n! / r! * (n - r) !

Where: n signifies the number of items, and r signifies the number of items being selected at a time.

Solution

1. 11C5 = 11! / 5! * (11-5) ! = 462 ways

2. 6C5 = 6! / 5! * (6-5) ! = 6 ways

3. 6/462 = 1/77 or 0.1230 is the probability that the selected group will consist of all men.