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 permutations of n objects taken r at a time?

Back

The formula is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects to arrange.

Front

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

Back

The formula is nCr = n! / [r!(n - r)!], where n is the total number of objects and r is the number of objects to choose.

Front

If you have 5 books and want to arrange 3 of them, how many arrangements can you make?

Back

60 arrangements (5P3 = 5! / (5-3)! = 60).

Front

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

Back

10 ways (5C2 = 5! / [2!(5-2)!] = 10).

Front

What does the term 'n!' represent?

Back

The term 'n!' (n factorial) represents the product of all positive integers up to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

Front

If you have 8 horses in a race, how many ways can you pick the first three places?

Back

336 ways (8P3 = 8! / (8-3)! = 336).

Front

What is the difference between permutations and combinations?

Back

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

Front

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

Back

60 ways (5P3 = 5! / (5-3)! = 60).