Question

**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?**

Answer #1

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?

A group of college students contains 7 seniors and 8
juniors.
a) In how many ways can 3 individuals from this group be chosen
for a committee?
b) In how many ways can a president, vice president, and
secretary be chosen from this group?
c) Suppose instead, there are n seniors and m juniors, for some
nonnegative integers n and m.
c-1) In how many ways can k individuals from this group be
chosen for a committee, for nonnegative integer...

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?

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...

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?

A bag contains 7 chocolate chip and 6 peanut butter cookies. How
many ways are there to choose either 4 chocolate chip or 4 peanut
butter?

There are 18 empty chairs in a room. How many different ways can
4 people be seated in the room?

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.

A department is composed of 10 men and 15 women. How many
different ways can a committee be created?
e with 6 members if:
(i) the committee do you have the same number of men as women?
(Count how to choose the
women, then how to choose men and use the Product Rule)
(ii) Do you have more women than men? (There are three cases,
calculate them and use the Sum Rule)
(iii) Explain why the tasks of creating a...

This question concerns forming committees of 4 persons from a
group of 10 people.
(a) How many ways are there to choose a committee of 4 persons
from a group of 10 persons, if order is not important?
(b) If each of these outcomes from part (a) is equally likely
then what is the probability that a particular person is on the
committee?
(c) What is the probability that a particular person is not on
the committee?
(d) How many...

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