Permutations & Combinations

Front

What is a permutation?

Back

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

Front

What is a combination?

Back

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

Front

How do you calculate permutations of n objects taken r at a time?

Back

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

Front

How do you calculate combinations of n objects taken r at a time?

Back

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

Front

In how many ways can a president, vice president, secretary, and treasurer be elected from a group of 30 students?

Back

The number of ways is P(30, 4) = 30! / (30 - 4)! = 30! / 26! = 30 × 29 × 28 × 27 = 423360.

Front

If Jacob and Eugene are planning trips to 4 countries from 14, how many different arrangements can they make?

Back

The number of arrangements is P(14, 4) = 14! / (14 - 4)! = 14 × 13 × 12 × 11 = 24024.

Front

How many combinations of shoes and socks can Robin make with 5 pairs of shoes and 6 pairs of socks?

Back

The total combinations are 5 × 6 = 30.

Front

What is the probability of drawing 4 cards of the same suit from a deck of cards?

Back

The number of ways to choose 4 cards of the same suit is 13C4 * 4 (for each suit) = 715 * 4 = 2860.

Front

What is the difference between permutations and combinations?

Back

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

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.