Product Rule for Counting

Front

What is the Product Rule for Counting?

Back

The Product Rule for Counting states that if there are 'm' ways to do one thing and 'n' ways to do another, then there are m × n ways to do both.

Front

If you roll a die (6 sides) and flip a coin (2 sides), how many possible outcomes are there?

Back

12 outcomes (6 sides of the die × 2 sides of the coin = 12 outcomes).

Front

How do you calculate the total number of combinations when choosing one item from multiple groups?

Back

Multiply the number of choices in each group together.

Front

A radio host has 12 songs on CD1, 14 on CD2, and 13 on CD3. How many different combinations of songs can be played?

Back

2184 combinations (12 × 14 × 13 = 2184).

Front

In a video game, if there are 3 levels, 4 time limits, and 6 avatars, how many different games can you play?

Back

72 different games (3 × 4 × 6 = 72).

Front

What is the formula to find the number of ways to choose a captain and co-captain from a team?

Back

The formula is n × (n - 1), where n is the number of players.

Front

How many ways can you choose a captain and co-captain from 11 players?

Back

110 ways (11 × 10 = 110).

Front

If an ice cream shop offers 3 types of cones and 31 flavors, how many different 1-scoop cones can be ordered?

Back

93 different cones (3 × 31 = 93).

Front

What is a combination in counting?

Back

A combination is a selection of items where the order does not matter.

Front

What is a permutation in counting?

Back

A permutation is an arrangement of items where the order does matter.