Combinations

Learn with an example

✈️ Stanley is filling up his pencil case before school. He wants to bring one pen and one pencil. He has purple, red, or green pens, and he has pencils decorated with pumpkins, dinosaurs, or dots. Given these choices, how many different combinations of items could Stanley put in his pencil case?

_____combinations

  • There are 3 pen colour choices and 3 pencil decoration choices. Multiply to find the number of possible combinations:
  • 3 × 3 = 9
    There are 9 combinations.
  • You could also make a list of all the combinations.
pen colourpencil decoration
purplepumpkins
purpledinosaurs
purpledots
redpumpkins
reddinosaurs
reddots
greenpumpkins
greendinosaurs
greendots
  • Now count the combinations. There are 9 combinations.

✈️ Eric is buying a new car. He can get a truck or a station wagon. The outside paint comes in green, purple, or white. Given these choices, how many different combinations does Eric have to choose from?

​_______combinations

  • There are 2 vehicle choices and 3 paint choices. Multiply to find the number of possible combinations:
  • 2 × 3 = 6
    There are 6 combinations.
  • You could also make a list of all the combinations.
vehiclepaint
a truckgreen
a truckpurple
a truckwhite
a station wagongreen
a station wagonpurple
a station wagonwhite
  • Now count the combinations. There are 6 combinations.

✈️ Tommy is buying a new car. He can get a van or a hatchback. The outside paint comes in blue, white, or purple. Given these choices, how many different combinations does Tommy have to choose from?

​_____ combinations

  • There are 2 vehicle choices and 3 paint choices. Multiply to find the number of possible combinations:
  • 2 × 3 = 6
    There are 6 combinations.
  • You could also make a list of all the combinations.
vehiclepaint
a vanblue
a vanwhite
a vanpurple
a hatchbackblue
a hatchbackwhite
a hatchbackpurple
  • Now count the combinations. There are 6 combinations.

Let’s practice!