Question

A group consists of six men and six women. Four people are selected to attend a conference.

a. In how many ways can four people be selected from this group of twelve ?

b. In how many ways can four women be selected from the six women?

c. Find the probability that the selected group will consist of all women?

Thank You please show work

Answer 1

a)

Four people selected from twelve by ¹²C₄ ways.

¹²C₄ = 12! / [ (12-4)! * 4! ]

= 495 ways

b)

4 women selected from 6 women by ⁶C₄ ways

⁶C₄ = 6! / [ (6-4)! * 4! ]

= 15 ways

c)

Probability that selected group consist of all women = ⁶C₄ / ¹²C₄

= 15 / 495

= 0.0303