Permutations and Combinations

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The number of permutations of n objects taken r at a time is given by n! / (n - r)!.

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 many ways can a disc jockey choose and arrange 3 songs from 9 songs?

Back

504 ways (calculated as 9P3 = 9! / (9-3)!).

Front

How many different combinations can 25 people form to advance to finals in a race?

Back

1,081,575 combinations (calculated as 25C8 = 25! / (8! * (25-8)!)).

Front

If Lucas owns 11 hoodies, how many ways can he choose 4 to bring on vacation?

Back

330 ways (calculated as 11C4 = 11! / (4! * (11-4)!)).

Front

How many ways can 68 juniors elect a president, vice president, and secretary?

Back

300,696 ways (calculated as 68P3 = 68! / (68-3)!).

Front

How many possible ways are there to place 18 runners in first, second, and third?

Back

4,896 ways (calculated as 18P3 = 18! / (18-3)!).

Front

What is the formula for permutations of n objects taken r at a time?

Back

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

Front

What is the formula for combinations of n objects taken r at a time?

Back

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

Front

What is the difference between permutations and combinations?

Back

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