Counting, Permutations & Combinations

Front

What is the definition of permutations?

Back

Permutations refer to the different arrangements of a set of items where the order matters.

Front

What is the definition of combinations?

Back

Combinations refer to the selection of items from a larger set where the order does not matter.

Front

How do you calculate the number of permutations of n items taken r at a time?

Back

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

Front

How do you calculate the number of combinations of n items taken r at a time?

Back

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

Front

If there are 4 candidates for mayor, 5 for city treasurer, and 2 for county attorney, how many ways can voters mark their ballots?

Back

40 ways (4 * 5 * 2 = 40).

Front

A fan has 6 games and 5 friends. How many ways can he take one friend to each game?

Back

15,625 ways (5^6 = 15,625).

Front

If 10 students each give a card to every other student, how many cards are given?

Back

90 cards (10 students * 9 cards each = 90).

Front

What is the difference between permutations and combinations?

Back

Permutations consider order, while combinations do not.

Front

In how many ways can you select 4 crayons from a box of 16?

Back

1,820 ways (C(16, 4) = 16! / (4! * 12!) = 1,820).

Front

What is the factorial of a number?

Back

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