Question

In: Statistics and Probability

A group consists of 6 men and 5 women. Four people are selected to attend a...

A group consists of 6 men and 5 women. Four people are selected to attend a conference.

a. In how many ways can 4 men be selected from this group of 11?

b. In how many ways can 4 men be selected from the 6 men?

c. Find the probability that the selected group will consist of all men. Would this be unusual?

Expert Solution

SOLUTION:

A group consists of 6 men and 5 women. Four people are selected to attend a conference.

Please note ⁿC_x = n! / [(n-x)!*x!]

a. In how many ways can 4 men be selected from this group of 11

The number of ways of selecting 4 men out of 11 = ¹¹C₄ = 11! / [(11-4)!*4!]

= 11!/(7!*4!)

= 330 ways

b. In how many ways can 4 men be selected from the 6 men?

4 mean cab be selected from the 6 men in ⁶C₄ ways = 6!/[(6-4)!*4!]

= 6!/(2!*4!)

= 15 ways

c. Find the probability that the selected group will consist of all men. Would this be unusual

Probability = Favourable outcomes/Total Outcomes

Favourable outcomes all 5 are men = ⁶C₅ = 6

Total Outcomes = 5 people out of 11 = ¹¹C₆ = 462

Therefore the required probability = 6/462 = 1 / 77 = 0.013

orchestra answered 2 years ago

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