Understanding Factorial Notation

Factorial notation is shorthand for multiplying consecutive descending natural numbers.

n! = n(n-1)(n-2) ... 3•2•1

NOTE: 0! = 1

Sample Problems:

A. 1. 3! = 2. 5!= 3. 7! =

B. List down all the possible ways of writing:

1. 3! = 2. 5!= 3. 7! =

A. Formula:

n! = n(n- 1)!

Solutions:

1. 3! =3•2•1 = 6

2. 5! =5•4•3•2•1= 120

3. 7! =7•6•5•4•3•2•1 = 5040

Equivalents

B. 1. n! with n = 3

n! = n(n- 1)!

3! = 3(3 -1)!

3! = 3(2)!

or

3! =3•2!

or

3! =3•2•1!

B. 2. n! with n = 5

n! = n(n- 1)!

5! = 5(5- 1)!

5! = 5(4)!

or

5! =5•4•3!

or

5! =5•4•3•2!

or

3! =5•4•3•2•1!

C. 3. n! = 7! with n = 7

7! = 7(7- 1)!

n! = n(n- 1)!

7! = 7(6)!

7! = 7•6!

or

7! =7•6•5!

or

7! =7•6•5•4!

or

7! =7•6•5•4•3!

or

7! =7•6•5•4•3•2!

or

7! =7•6•5•4•3•2•1!