Fundamental Counting Principle & Permutations

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 do both.

Front

How do you calculate the number of outfits possible with multiple clothing items?

Back

Multiply the number of choices for each item. For example, with 5 jeans, 8 t-shirts, 2 shoes, and 3 hats: 5 × 8 × 2 × 3 = 240 outfits.

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The order matters in permutations.

Front

How many ways can you arrange the letters in the word 'MATH'?

Back

There are 4! (4 factorial) ways to arrange the letters, which equals 24.

Front

What is the formula for permutations of 'n' objects taken 'r' at a time?

Back

The formula is P(n, r) = n! / (n - r)!.

Front

How do you calculate the number of ways to select a president, vice president, and secretary from a group?

Back

Use permutations since the order matters. For 5 people: P(5, 3) = 5! / (5 - 3)! = 60.

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not.

Front

How do you find the total number of meal combinations from different food choices?

Back

Multiply the number of choices for each category. For example, 2 salads, 3 entrees, and 2 beverages: 2 × 3 × 2 = 12 combinations.

Front

How many different versions of a car model can be created with multiple options?

Back

Multiply the number of options for each feature. For example, 4 trims, 5 colors, and 3 interiors: 4 × 5 × 3 = 60 versions.

Front

What is the factorial of a number?

Back

The factorial of a number 'n' (denoted as n!) is the product of all positive integers up to 'n'.