Permutations Vs Combinations and Factorals

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 the factorial of a number n (n!)?

Back

The factorial of a number n is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

Front

What is the value of 0! (zero factorial)?

Back

0! = 1 by definition.

Front

If you have 10 different books and want to arrange 3 of them on a shelf, how do you calculate this?

Back

Use permutations: P(10, 3) = 10! / (10-3)! = 10 × 9 × 8 = 720.

Front

If you want to choose 3 books from a set of 10 without regard to order, how do you calculate this?

Back

Use combinations: C(10, 3) = 10! / (3!(10-3)!) = 120.

Front

What is the difference between permutations and combinations?

Back

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

Front

Evaluate: (5!) / (3!)

Back

(5!) / (3!) = (5 × 4 × 3 × 2 × 1) / (3 × 2 × 1) = 20.

Front

Expand 5!

Back

5! = 5 × 4 × 3 × 2 × 1 = 120.

Front

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

Back

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