Counting Methods

Question 0

What is a factorial?

Answer 0

A symbol that is often used with the multiplication principle.

If n is an integer greater than 1, then n factorial, denoted by the symbol n!, is defined as the product of all the integers from 1 through n.

Example:

2!=(1)(2)=2
3!=(1)(2)(3)=6
4!=(1)(2)(3)(4)=24, etc.

Also, 0!=1!=1.

Question 1

Name a fundamental principle of multiplication used in counting methods.

Answer 1

“If a first object can be chosen in m ways and a second object may be chosen in n ways, then there are mn ways of choosing both objects.

Question 2

Define combination.

Answer 2

The number of possible selections of k objects at a time. It is denoted by (n k).

The value of (n k) is given by n!/k!(n-k)!.