Question

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.

Answer #1

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?

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?

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

How many different committees can be formed from 6 teachers and
32 students if the committee consists of 3 teachers and 3
students?
In how many ways can the committee of 6 members be selected?

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?

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?

There are 9 children - 6 girls and 3 boys - a kindergarten
classroom having 3 rows of chairs, 3 chairs in each row. (a) How
many ways can the children be seated in the chairs? (b) How many
ways can the children be seated with all the boys seated together
in a row?

4. Your science group has 9 boys and 12 girls in it. You want
them to work on a project together. (9 points)
a. How many
different groups of 3 can you create?
b. How many
different groups of 6 can you create if you want 3 boys and 3 girls
in the group?
c. What is the
probability that a four person social committee will consists of
all girls?

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?

Ten high school students, 6 girls and 4 boys, have applied for 5
available scholarships. In how many ways can these scholarships be
awarded among the applicants if a) No preference is given to any
one student? b) One particular student must be awarded an
assistantship? c) The group of applicants includes 6 girls and 4
boys and it is stipulated that a majority of girls must be awarded
scholarships? d) At least 2 boys are awarded?e) At most 2...

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