10.1 Fundamental Counting Principle

Front

What is the Fundamental Counting Principle?

Back

The Fundamental Counting Principle states that if there are 'm' ways to do one thing and 'n' ways to do another, then there are m × n ways to perform both actions.

Front

How do you calculate the number of combinations when choosing items without replacement?

Back

When choosing items without replacement, the number of combinations is calculated by multiplying the number of choices available for each selection.

Front

If a lock has 60 numbers and you need to choose 3 in sequence without repetition, how many combinations are there?

Back

The number of combinations is calculated as 60 × 59 × 58 = 205,320.

Front

What operation is used with the Fundamental Counting Principle?

Back

Multiplication.

Front

How many meal combinations can you create with 6 appetizers, 22 entrees, and 3 desserts?

Back

The number of combinations is 6 × 22 × 3 = 396.

Front

If you have 50 history books, 95 fantasy novels, and 30 science books, how many ways can you choose 1 history book, 2 science books, and 1 fantasy book?

Back

The number of combinations is calculated as 50 × (30 choose 2) × 95 = 4,132,500.

Front

What is the formula for combinations when selecting 'r' items from 'n' items?

Back

The formula is C(n, r) = n! / (r!(n-r)!), where '!' denotes factorial.

Front

What is a factorial?

Back

A factorial, denoted as n!, is the product of all positive integers up to n.

Front

How many different ways can you arrange 3 books on a shelf?

Back

The number of arrangements is 3! = 6.

Front

If you can choose from 22 toppings and you want to select 3 different toppings, how do you calculate the combinations?

Back

Use the combination formula: C(22, 3) = 22! / (3!(22-3)!) = 1540.