Permutation and Combination Flashcard

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

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

Back

The formula is n! / (n - r)!. This calculates the number of ways to arrange r objects from a set of n.

Front

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

Back

The formula is n! / (r! * (n - r)!). This calculates the number of ways to choose r objects from a set of n without regard to order.

Front

What does 5! (5 factorial) represent?

Back

5! = 5 × 4 × 3 × 2 × 1 = 120. It represents the total number of ways to arrange 5 distinct objects.

Front

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

Back

0! = 1. By definition, the factorial of zero is one.

Front

In the expression nPr, what does 'r' represent?

Back

'r' represents the number of objects being selected or arranged from a total of 'n' objects.

Front

If you have 6 countries and want to choose 4 to visit, what concept applies?

Back

This is a combination problem because the order of countries does not matter.

Front

How many ways can you arrange the letters in the word 'math'?

Back

There are 24 ways to arrange the letters in 'math' (4! = 24).

Front

What is the difference between permutations and combinations?

Back

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