Question

In a club with 12 male and 12 female members, how many 5-member committees can be chosen that have

(a) at least 4 women?

(b) no more than 2 men?

Answer #1

12 male and 12 female. And a 5-membered committee is to be formed.

a) Atleast 4 women means : either 4 or 5 women.

case1) So if we choose 4 women and 1 man then the number of ways are

case2) If we choose all 5 women then the number of ways are

So total number of ways is=5940+792=6732 answer

b) No more than two men means that either 2 or 1 or no men.

case3) If we take 2 men, then 3 will be women andthe number of ways will be

case4) If we take 1 man and 4 women, then it is similar to case1) and the number of ways is 5940.

case5) I we take no man, then we take all women which is similar to case2) and the number of ways is 792.

Hence total number of ways in this part is 14520+5940+792=21252 answer.

In a club with 9 male and 13 female members, a 3-member
committee will be randomly chosen. Find the probability that the
committee contains at least 2 women.

A university has 90 faculty members: 60 male and 30 female. How
many committees of size 18 can we form if:
(a) no restriction?
(b) among the selected 18 faculty members, one position is
president and one is vice president?
(c) among the selected 18 faculty members, one position is
president and tow are vice presidents?
(d) among the selected 18 faculty members, one position is
president, one is a male vice president and one is a female vice
president?

How many
ways can a committee of 2 be selected from a club with 12
members?

How many 6-member committees can be
formed from 8 girls and 9 boys if the following are true?
a)There must be exactly 3 girls
b)There are no conditions
c)There must be at least 4 boys.

a
committee of 5 ppl is to be chosen from the following department. 4
faculty members in CS and enginerring, 5 in electrical engineering,
6 in mechanical engineering, and 3 aerospace engineering.
a) how many committees are possible?
B) how many committees with at least 2 faculty members from
CSE?

The Board of Directors at Smallville National Bank consists of
12 members - 9 male and 3 female. A revised mortgage policy manual
is planned and a committee of 3 Board members will prepare the
manual and be selected randomly.
a. What is the probability that all committee members will be
male
b. What is the probability that at least one member will be
female?

Independent random samples were taken of male and female members
of University Entrepreneurship Club. These members were considering
starting a business. Of 350 members, 150 actually started a
business venture.
a) Estimate the value of the population proportion. (Round your
answers to 3 decimal places.)
b)Develop a 90% confidence interval for the population
proportion.

Independent random samples were taken of male and female members
of University Entrepreneurship Club. These members were considering
starting a business. Of 500 members, 200 actually started a
business venture.
a. Estimate the value of the population proportion. (Round
your answers to 3 decimal places.)
b. Develop a 99% confidence interval for the population
proportion.

A
committe od five people is to be chosen from a club that boast a
membership of ten men and 12 women. how many can the committee be
formed if it is to contain atleast two men and two women?how many
if in addition , one particular man and one woman who are members
of the club refuse to serve together on the committee?
prove that (n choose r ) = (n choose n-r) by using a
combinatorial argument.

A committee of 4 people is chosen from 9 women and 9 men. How
many different committees are possible that consist of 2 women and
2 men?

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