Factorials

Question 1

What are factorials used for?

Answer 1

Used for arranging and counting possibilities

Example; You have five books and want to know how many different ways they can be arranged. We can use the factorial of 5 (5!) to calculate this. 5! = 5 x 4 x 3 x 2 x 1 = 120, so there are 120 ways you could organise them.

Question 2

How do you calculate the number of ways to pick 2 books from 5?

Answer 2

5! / [ 2! ( 5 - 2 )! ] = 10

This is derived from the formula n! / [ r! ( n - r )! ] where n is the total number of items and r is the number of items you are choosing.

Question 3

What does n represent in the formula n! / [ r! ( n - r )! ]?

Answer 3

Total number of items

Question 4

What does r represent in the formula n! / [ r! ( n - r )! ]?

Answer 4

Number of items you are choosing

Question 5

What does n - r represent in the formula n! / [ r! ( n - r )! ]?

Answer 5

Number of items you’re not choosing

Question 6

Fill in the blank: x ( x - 1 )! = _______

Answer 6

x!

Question 7

Fill in the blank: x! ( x + 1 ) = _______

Answer 7

( x + 1 )!

Question 8

What is the simplified expression for x! + ( x + 1 )!?

Answer 8

x! ( x + 2 )

Derived from the equation x! + x! ( x + 1 ) = x! ( 1 + x + 1 ).

Question 9

What is the result of ( n + 2 )! - n!?

Answer 9

n! ( n^2 + 3n + 1 )

This is simplified from ( n + 2 ) ( n + 1 ) n! - n!.

Question 10

True or False: 5! = 120.

Answer 10

True

Question 11

What is the factorial of 5 (5!)?

Answer 11

5 x 4 x 3 x 2 x 1 = 120