Question

Consider a class with 8 boys and 6 girls.

a) In how many ways can a committee of nine consisting of 4 boys and 5 girls be chosen?

b) How many of the possible ways a committee of 7 can be chosen at random from the class consists at least 3 girls?

Answer #1

In a class, there are 10 boys and 8 girls.
(a) In how many ways can the teacher arrange 6 boys and 4 girls
in a row if the girls must stand in the middle of the row?
(b) In how many ways can the teacher arrange 6 boys and 4 girls
in a row if no girls stand next to another girl?

Suppose that a class consists of 8 girls and 10 boys. How many
ways are there to form a team with 5 members if..
A) It must contain exactly three boy's?
B) It must contain at most one girl?

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.

Sixteen boys and nine girls go on a camping trip. In how many
ways can a group of sic be selected to gather firewood, giveen the
following conditions?
a. The group consist of two girls and four boys.
b. The group contains at least two girls.
c. The group contains at least one girl and one boys.

In how many ways can five girls be chosen from a class of twenty
if the class prefect must be included?
Full explanation, please.

A team of 8 boys and 5 girls. how many different teams
are possible if there must be two boys and two girls? how many
different teams are possible if they must all be girls?

A school committee of 9 is being formed from a class
consisting of 7 males and 6 females. How many different committees
can be formed if there / are is
a) at least one girl
b) as many girls as there is boys

1. In how many ways can 10 objects be split into two
groups containing 4 and 6 objects, respectively?
2. In how many ways can a committee of 5 people be chosen out of 9
people?
3. Out of 5 mathematicians and 7 physicists, a committee consisting
of 2 mathematicians and 3 physicists is to be formed. In how many
ways can this be done if (a) any mathematician and any physicist
can be included, (b) one particular physicist must...

There are 18 students in this class….5 girls, 13 boys.
1. What is the probability that a group of 5 boys will be
chosen?
2. What is the probability that at least 2 girl will be chosen
for a group of 3?
3. What is the probability that 7 or less boys will be chosen
for a group of 10?

12 girls and 19 boys (total 31) are running for 6 positions on
the school's Graduation Committee. 3 of the 12 girls are sisters
and each candidate is equally likely chosen. Calculate the
following:
a) What is the probability that all 3 sisters will be on the
committee?
b)What is the probability that at least 1 of the sisters will be
on the committee?
c)What is the probability that it will be an all boys
committee?

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