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

What is 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

How do you calculate permutations of n objects taken r at a time?

Back

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

Front

How do you calculate combinations of n objects taken r at a time?

Back

The formula for combinations is C(n, r) = n! / [r!(n - r)!].

Front

What is 6! (6 factorial)?

Back

6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.

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.

Front

If you have 10 students and want to choose 3 for a team, how many combinations are there?

Back

C(10, 3) = 10! / [3!(10 - 3)!] = 120 combinations.

Front

In how many ways can you arrange the letters in the word 'MATH'?

Back

There are 4! = 24 ways to arrange the letters in 'MATH'.

Front

What is the difference between permutations and combinations?

Back

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