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

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...

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 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?

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...

How many:
ways can an exam consisting of 10 true and false questions be
answered?
ways can an exam consisting of 5 true and false questions
followed by 2 multiple choice questions with four choices each be
answered?
4-digit numbers are there?
New York license plates can be made that consist of 3 letters
followed by 4 numbers?
New York license plates can be made that consist of 3 letters
followed by 4 numbers given the restriction that if the...

In how many ways can 8 books be arranged on a shelf if a. any
arrangement is possible, b. 3 particular books must always stand
together, c. two particular books must occupy the ends?

Circular Permutations and Permutations with Similar Elements
1) In how many ways can three people be made to sit at a round
table?
2) In how many ways can three couples be seated at a round
table, so that men and women sit alternately?
3) In how many ways can five keys be put on a key ring?
4) Find the number of different permutations of the letters of
the word MATHEMATICS.
5) How many different ways can three pennies,...

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