Chapter 13, Problem 21RE

Forming Committees A group of 9 people is going to be formed into committees of 4, 3, and 2 people. How many committees can be formed if:

a. A person can serve on any number of committees?

b. No person can serve on more than one committee?

To determine

To find: How many committees can be formed if,

a. A person can serve on any number of committees?

Answer to Problem 21RE

a. 381024

Explanation of Solution

Given:

A group of 9 people is going to be formed into committees of 4, 3, and 2 people.

Formula used:

$C\left(n, r\right) = \frac{n!}{r!\left(n - r\right)!}$

Calculation:

A group of 9 people is going to be formed into committees of 4, 3, and 2 people.

a. A person can serve on any number of committees.

Number of committees that can be formed is $= C\left(9, 4\right) \&*\#x00A0;C\left(9, 3\right) \&*\#x00A0;C\left(9, 2\right)$

$= \frac{9!}{4!\left(9 - 4\right)!} \&*\#x00A0;\frac{9!}{3!\left(9 - 3\right)!} \&*\#x00A0;\frac{9!}{2!\left(9 - 2\right)!}$

$= \frac{9!}{4 ! 5 !} \&*\#x00A0;\frac{9!}{3 ! 6 !} \&*\#x00A0;\frac{9!}{2 ! 7 !}$

$= 126 \&*\#x00A0;84 \&*\#x00A0;36$

$= 381024$

To determine

To find: How many committees can be formed if,

b. No person can serve on more than one committee?

Answer to Problem 21RE

b. 1260

Explanation of Solution

Given:

A group of 9 people is going to be formed into committees of 4, 3, and 2 people.

Formula used:

$C\left(n, r\right) = \frac{n!}{r!\left(n - r\right)!}$

Calculation:

A group of 9 people is going to be formed into committees of 4, 3, and 2 people.

b. A person can serve on any number of committees.

Number of committees that can be formed is $= C\left(9, 4\right) \&*\#x00A0;C\left(5, 3\right) \&*\#x00A0;C\left(2, 2\right)$

$= \frac{9!}{4!\left(9 - 4\right)!} \&*\#x00A0;\frac{5!}{3!\left(5 - 3\right)!} \&*\#x00A0;\frac{2!}{2!\left(2 - 2\right)!}$

$= \frac{9!}{4 ! 5 !} \&*\#x00A0;5 \&*\#x00A0;2 \&*\#x00A0;1$

$= 126 \&*\#x00A0;10$

$= 1260$