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

Define a permutation.

Back

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

Front

Define a combination.

Back

A combination is a selection of objects where the order does not matter. It focuses on the group rather than the arrangement.

Front

How many ways can you choose 3 desserts from 8 options?

Back

56 ways (using combinations: C(8,3) = 8! / (3!(8-3)!) = 56).

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

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

Back

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

Front

If a license plate consists of 3 letters followed by 2 numbers, how many different plates can be made if repeats are allowed?

Back

1,757,600 plates (26^3 * 10^2 = 1,757,600).

Front

How many ways can a coach choose 5 players from a team of 11?

Back

462 ways (using combinations: C(11,5) = 11! / (5!(11-5)!) = 462).

Front

What is the difference between permutations and combinations?

Back

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

Front

How many different arrangements can be made with the letters in the word 'RHOMBUS'?

Back

840 arrangements (using permutations: 7! / (7-4)! = 840).