Understanding Combinations and Factorials

Go for a run

Have a meal at ShmoopDonald's

Watch a movie

Take a nap

Five

Four

Three

Two

Guilty

Happy

Excited

Indifferent

To return the food

To eat two out of four items

To eat all the items

To eat only one item

A selection where order matters

A selection where order doesn't matter

A sequence where order matters

A sequence where order doesn't matter

n choose r equals n factorial divided by n minus r factorial times r factorial

n choose r equals n factorial times r factorial

n choose r equals n plus r factorial

n choose r equals n minus r factorial divided by n factorial

The number of combinations

The factorial of the number of items

The total number of items

The number of items in a combination

12

16

32

24

4

3

2

1

6

7

4

5