Question

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 be on the
committee, (c) two particular mathematicians cannot be on the
committee?

4. How many different salads can be made from lettuce, escarole,
endive, watercress, and chicory?

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?

How many possible outcomes exist in the following
situations?
(a) A board of 3 mathematicians and 3 physicists is to be
selected from a group of 6 mathematicians and 7 physicists.
(b) During a dinner consisting of several courses, a guest can
choose a starter (soup or salad), a main course (meat, ﬁsh or
tofu), side dish (rice, pasta or potatoes) as well as a dessert
(apple pie or chocolate ﬂan).
(c) In a restaurant kitchen a salad plate is...

There are 7 women and 5 men in a department. (a) How many ways
can a committee of 4 people be selected if there must be 2 men and
2 women on the committee? (b) If a committee is formed at random,
what is the probability that it is made up of 2 men and 2
women.

4 people are to be chosen from 10 men and 12 women to form a
committee which contains at least two women. How many different
ways can the committee be formed? If, among the 10 men and 12
women, Mr. and Mrs. Smith can not both be selected, then how many
different ways can the committee be formed?

A) How many permutations of 7 objects, taking 3 at a time?
Group of answer choices: 210, 35, 5040, 6
B) How many ways can 4 books be arranged on a shelf, if they can
be selected from 12 books?
C) How many ways can a committee of 4 people be selected from a
group of 8 people?
D) If the letters A, B, C, D, E, and F are to be used in a
five-letter code, how many different...

Suppose you have a room that contains 6 chimps and 4
orangutans.
a) How many ways can you choose a ‘committee’ of 5
primates with no restrictions?
b) How many ways can you choose a committee that
contains no orangutans? What is the probability?
c) How many ways can you choose a committee that has 4
orangutans? What is the probability?

I was wondering - how many different possible ways can you make
groups of 3 if you have 15 people in total? It's important to note
that two these people absolutely cannot be in the same group
together. Thanks a bunch!

In how many ways could eight students be placed into
two groups of any size,as long as there are at least two in a
group?Explain your reasoning.

1. Twelve individuals want to form a committee of four.
(a.) How many committees are possible?
(b.) The 12 individuals consist of 5 biologists, 4 chemists, and
3 physicists. How many committees consisting of 1 biologist, 1
chemist, and 2 physicists are possible?
(c.) In the setting of part (b), if all committees are equally
as likely, what is the probability the committee formed will
consist of 1 biologist, 1 chemist, and 2 physicists?
2. You are out of town...

In
how many ways can 2 red and four blue rooks be placed on am 8 by 8
board so that no 2 rooks can attack one another ?
A roller coaster has 5 cars containing 4 seats 2 in frony and
2 in the back, there are 20 people ready for a ride, how many ways
can the ride begin? what if a certain 2 people want to seat in
different cars?

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