Permutations and 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. It focuses on the group rather than the arrangement.

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

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.

Front

If a disc jockey has 9 songs and chooses 3 to arrange, how many arrangements are possible?

Back

504 arrangements.

Front

How many ways can a team of 17 players choose 3 players?

Back

680 ways.

Front

In how many different orders can 8 glasses of water be arranged?

Back

8! (factorial) ways.

Front

How many ways can 10 members choose 3 officers (captain, co-captain, secretary)?

Back

720 ways.

Front

What is the significance of the order in permutations?

Back

In permutations, the order of selection is crucial; different orders count as different arrangements.