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?

Solutions

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 1 year ago

Next > < Previous

Related Solutions

4. A group consist of 6 men and 5 women. Find the number of choosing 5...

4. A group consist of 6 men and 5 women. Find the number of choosing 5 committee members: e) Without condition f) Must have 2 men and 2 women and another person either men or women g) The number of men must exceed the number of women h) Must have at least 1 men and 1 women 6. How many choices are there if we want to make a 5 person committee from 12 persons, if the president has already...

10). From a group of 6 men and 8 women a committee consisting of 4 men...

10). From a group of 6 men and 8 women a committee consisting of 4 men and 3 women is to be formed. How many different committees are possible if: a. 2 of the men refuse to serve together? b. 2 of the women refuse to serve together? c. 1 man and 1 woman refuse to serve together?

A committee of size 3 is to be selected from 6 men and 2 women. (a)...

A committee of size 3 is to be selected from 6 men and 2 women. (a) Find the probability distribution of the number of women selected in the committee, and (b) Find the standard deviation. *

From a group of 4 women and 6 men, a committee of 4 members will be...

From a group of 4 women and 6 men, a committee of 4 members will be elected. a) How many committees can you choose? b) How many committees can be elected if there should be 3 men? c) How many committees can be elected if there should be at least one woman? d) If you want to choose a directive, that is, a president, vice president, treasurer and secretary, in how many ways can you choose? e) If the whole...

A committee of 2 women and 6 men is to be chosen randomly from a group...

A committee of 2 women and 6 men is to be chosen randomly from a group of 18 women and 13 men. a) What is the probability that "Ann" (female) and her friend "Bob" (male) are on the committee together? b) What is the probability that ``Ann''(female) and her friend ``Bob''(male) are on the committee and their friends ``Carla''(female) and ``Dan''(male) are also on the committee? c) Given that ``Carla'' and ``Dan'' have been chosen to be on the committee,...

Six people are in a room, 3 men and 3 women, and two individuals are selected....

Six people are in a room, 3 men and 3 women, and two individuals are selected. What is the probability of both being women, given that one is a woman? What is the probability of both being women, given that one is a specific woman?

A class in probability theory consists of 3 men and 5 women. An exam is given,...

A class in probability theory consists of 3 men and 5 women. An exam is given, and the students are ranked according to their performance. Assuming that no two students obtain the same score, and all rankings are considered equally likely. 1.The probability that women receive the bottom 5 scores is 2.The probability that the top grade and the bottom grade are for men is

from a group of 8 women and 5 men a committee of 4 members will be...

from a group of 8 women and 5 men a committee of 4 members will be elected a) how many committees can you choose? b)How many committees can be elected if there should be 3 men? c)How many committees can you choose if there should be at least one woman? d)If you want to elect a board, that is, a president, vice president, treasurer, secretary, in how many ways can you choose? e)If you want to take a photo of...

A committee of 4 is chosen at random from a group of 7 women 5 men....

A committee of 4 is chosen at random from a group of 7 women 5 men. Find the probability that the committee contains at least one man. without replacement

If 3 Men or 4 Women Can Plow a Field in 43 Days, How Long Will 6 Men and 5 Women Plow It?

If 3 Men or 4 Women Can Plow a Field in 43 Days, How Long Will 6 Men and 5 Women Plough It?

Subjects