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.

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

Calculate 5!

Back

5! = 5 × 4 × 3 × 2 × 1 = 120.

Front

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

Back

There are 504 ways to choose and arrange 3 songs from 9.

Front

How many 2-digit numbers can be formed using the digits 1, 2, 3, and 4 without repetition?

Back

12 different 2-digit numbers can be formed.

Front

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

Back

8! = 40,320 different orders.

Front

What is the significance of the top finishers in a race?

Back

The top finishers determine who advances to the finals, which can be calculated using combinations.