Question

Consider 12 people (5 men and 7 women).

1. How many ways are there of forming teams of 5, if the team must
consist of 3 men and 2 women? How many if it must consist of at
least one man? How many if it must contain at most one man?

Answer #1

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?

7). 13 players for a softball team show up for a game:
a. How many ways are there to choose 10 players to take the
field?
b. How many ways are there to assign the 10 positions by
selecting players form the 13 people who show up?
c. Of the 13 people who show up, 3 are women. How many ways are
there to choose 10 players to take the field if at least one of
these players must be...

A committee of 4 people is chosen from 9 women and 9 men. How
many different committees are possible that consist of 2 women and
2 men?

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,...

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?

In how many ways can 16 people stand in a circle?
In how many ways can 16 people stand in a line?
Suppose that 8 of the people are men and 8 are women. In how
many ways can they stand in a circle assuming
that they alternate in gender?
In how many ways can 8 men and 8 women stand in a line,
alternating in gender?

Suppose that a town has 100 ill people: 25 children, 41 men, and
34 women.
(a) In how many ways can 14 children and 16 women be selected
from this group for transport to the nearest hospital?
(b) Suppose that 14 children and 16 women have been selected and
transported to the hospital, where beds
number 23 to 69 are available for new patients. In how many ways
can they be assigned to beds?
(c) In how many ways can...

A group consists of seven men and six women. Five people are
selected to attend a conference.
a. In how many ways can five people be selected from this group
of thirteen?
b. In how many ways can five women be selected from the six
women?
c. Find the probability that the selected group will consist of
all women.
(Type an integer or a simplified fraction.)

A group contains n men and n women, where n is a positive
integer.
a) How many ways are there to arrange these people in a row if
there are no restrictions on where they sit?
b) How many ways are there to arrange these people in a row if
the men and women alternate?
c) If people are seated randomly, what is the probability that a
man will be seated in the first seat?
d) If people are seated...

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