Fundamental Counting Principle, Permutations, & Combinations

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

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The number of permutations of 'n' objects taken 'r' at a time is given by nPr = n! / (n - r)!.

Front

What is a combination?

Back

A combination is a selection of objects without regard to the order. The number of combinations of 'n' objects taken 'r' at a time is given by nCr = n! / [r!(n - r)!].

Front

How many ways can you choose 2 jellybeans from 15 unique jellybeans?

Back

15C2 = 105 ways.

Front

How would you solve: A car model is available in 9 colors, 3 styles, and 2 sizes. How many ways can you order the car?

Back

Using the Fundamental Counting Principle: 9 × 3 × 2 = 54 ways.

Front

How many different teams of 4 can be selected from 15 students?

Back

15C4 = 1365 different teams.

Front

How many different versions of a car model with 4 trims, 5 colors, and 3 interiors can be created?

Back

Using the Fundamental Counting Principle: 4 × 5 × 3 = 60 different versions.

Front

What is the value of 8! (8 factorial)?

Back

8! = 40320.

Front

What is the formula for permutations?

Back

The formula for permutations is nPr = n! / (n - r)!.

Front

What is the formula for combinations?

Back

The formula for combinations is nCr = n! / [r!(n - r)!].