Permutation and combination

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

When do you use permutations?

Back

Use permutations when the arrangement or order of the items is important, such as in races where medals are awarded.

Front

When do you use combinations?

Back

Use combinations when the arrangement does not matter, such as selecting a group of people.

Front

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

Back

6 ways (3! = 3 x 2 x 1 = 6).

Front

How many ways can you choose 2 fruits from a selection of 5?

Back

10 ways (5 choose 2 = 5! / (2!(5-2)!) = 10).

Front

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

Back

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

Front

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

Back

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

Front

How many different pizzas can you make with 8 meats, 4 cheeses, 3 crusts, and 2 sauces?

Back

192 different pizzas (8 x 4 x 3 x 2 = 192).

Front

How many ways can 40 runners finish in the top 3 positions?

Back

The answer is 12,480 ways (P(40, 3) = 40! / (40-3)! = 40 x 39 x 38).