Permutation & Combination

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The number of permutations of n distinct objects is n! (n factorial).

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 n! / (r!(n-r)!).

Front

How do you calculate the number of distinguishable arrangements of a word with repeated letters?

Back

The formula is n! / (n1! * n2! * ... * nk!), where n is the total number of letters, and n1, n2, ..., nk are the frequencies of the repeated letters.

Front

What is the factorial of a number?

Back

The factorial of a non-negative integer n, denoted as n!, is the product of all positive integers less than or equal to n.

Front

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

Back

The number of arrangements is 3! = 6.

Front

If you have 5 different colored balls, how many ways can you choose 2?

Back

The number of combinations is 5! / (2!(5-2)!) = 10.

Front

What is the difference between permutations and combinations?

Back

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

Front

How many different ways can first, second, and third prize be awarded among 6 participants?

Back

The number of ways is 6P3 = 6! / (6-3)! = 120.

Front

If you have 4 types of dinosaurs and 2 colors, how many different models can you create?

Back

This is a combination of types and colors, resulting in 4 * 2 = 8 models.

Front

What is the total number of outcomes for picking a day of the week and a month of the year?

Back

There are 7 days in a week and 12 months in a year, so the total outcomes are 7 * 12 = 84.