Question

How many ways are there to select a committee of 17 politicians chosen from a room full of indistinguishable Democrats, indistinguishable Republicans, and indistinguishable Independents if every party must have at least two members on the committee? If, in addition, no group may have a majority of the committee members?

Answer #1

From 10 people how many ways are there to select a committee
consisting of a chairman, vice-chair, and three other committee
members?

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 committee of four is to be chosen from a group of six men and
seven women.
a) How many different committees are possible?
b) What is the probability that committee consists of two men
and two women?
c) What is the probability that committee consists of at least
two women?

There are 21 novels, 18 volumes, and 16 comic books on a shelf.
How many ways can you select one novel, one volume, and one
comic?
How many ways can a four-person executive committee (president,
vice-president, secretary, treasurer) be selected from a 16-member
board of directors of a non-profit organization? The order
matters.
A group of 8 politicians is to be chosen from a candidate list
of 19 to represent the city council. How many ways can this be
done?...

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

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

Exercise 1-36Twenty-five girls are bored.
(a) In how many ways may five girls be chosen to go to a party
and five different girls
be chosen to volunteer at a soup kitchen (and the remaining 15
girls stay home)?
(b) How many ways may the girls form two teams of 5 to play
basketball against each other?
the answers are 823,727,520 and 411,863,760 I just need the
work

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?

Suppose that a department contains 11 men and 16 women. How many
ways are there to form a committee with 6 members if it must have
strictly more women than men?

An organization consisting of 27 women and 17 men needs to
select from its ranks a committee of 6 people. In how many possible
ways can the committee be formed so that it contains exactly two
men?

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