05-08-2024 Factorial, Permutations & Combinations

Front

What is a combination?

Back

A combination is a selection of items from a larger set where the order does not matter. For example, choosing 4 students from a class committee.

Front

What is a permutation?

Back

A permutation is an arrangement of items where the order matters. For example, selecting a President, Vice President, and Treasurer from a group.

Front

What does 4! (4 factorial) represent?

Back

4! = 4 × 3 × 2 × 1 = 24. It represents the product of all positive integers up to 4.

Front

Evaluate: (24/6)!

Back

(24/6)! = 4! = 24.

Front

Calculate: 6! ÷ 3!

Back

6! ÷ 3! = 720 ÷ 6 = 120.

Front

What is the formula for combinations?

Back

The formula for combinations is C(n, r) = n! / (r!(n-r)!), where n is the total number of items, and r is the number of items to choose.

Front

What is the formula for permutations?

Back

The formula for permutations is P(n, r) = n! / (n-r)!, where n is the total number of items, and r is the number of items to arrange.

Front

What is the difference between combinations and permutations?

Back

The difference is that combinations do not consider the order of selection, while permutations do.

Front

What is 0! (zero factorial)?

Back

0! = 1 by definition.

Front

If you have 5 books and want to arrange them on a shelf, how many permutations are there?

Back

There are 5! = 120 permutations.