Permutations, Combination, and Counting (Take 2)

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

Calculate 4! (4 factorial).

Back

4! = 4 × 3 × 2 × 1 = 24.

Front

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

Back

The number of arrangements is 3! = 6.

Front

If a club has 5 members, how many ways can they choose a president and a vice president?

Back

There are 5 choices for president and 4 remaining choices for vice president, so 5 × 4 = 20 ways.

Front

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

Back

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

Front

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

Back

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

Front

How many different ways can 8 swimmers finish a race if prizes are awarded for 1st, 2nd, and 3rd place?

Back

There are 8 × 7 × 6 = 336 different outcomes.

Front

If you have 4 different skirts, 3 different blouses, and 2 pairs of shoes, how many outfits can you create?

Back

You can create 4 × 3 × 2 = 24 different outfits.

Front

What is the value of 7! (7 factorial)?

Back

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.