Permutations and Combinations Quiz

What is the difference between a permutation and a combination?

• Permutation is about arranging things in different order, while combination is about combining things

• Permutation is about rearranging things, while combination is about selecting things

• Permutation is about combining things, while combination is about arranging things in different order

• Permutation is about selecting things, while combination is about rearranging things

Answer explanation

Permutation is about arranging things in different order, while combination is about combining things

How many different ways can you arrange three books on a shelf from a group of seven?

• 20

• 30

• 42

• 60

Answer explanation

There are 7 books to choose from for the first position, then 6 for the second, and 5 for the third. So the total number of arrangements is 7 * 6 * 5 = 210. However, since the order of the books on the shelf matters, the correct answer is 20.

Anika, Mia, and Kai are in a math competition. They are asked to calculate the number of ways they can arrange themselves for a group photo. What is the formula they should use for calculating these permutations?

• nPr = n! / (n + r)!

• nPr = n! / r!

• nPr = n! / (n - r)!

• nPr = n! * r!

Answer explanation

The formula for calculating permutations is nPr = n! / (n - r)!. This formula accounts for the number of ways to arrange objects without repetition and highlights the correct choice.

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

• 420

• 120

• 210

• 252

Answer explanation

There are 210 different ways to arrange the letters in the word 'alabama'.

Sophia, Charlotte, Benjamin and 9 other engineers are part of a project team. How many different teams of four can be produced from this pool of 12 engineers?

• 495

• 440

• 330

• 220

Answer explanation

There are 12 engineers and we need to choose 4. The number of different teams is given by the combination formula C(12, 4) = 495. Therefore, the correct answer is 495.

James, Grace, and Abigail are planning a party and they want to invite their friends. If they want to calculate the number of ways they can invite a certain number of friends, which formula should they use for combinations?

• nCr = n! / r!

• nCr = n! * r!

• nCr = n! / (n - r)!

• nCr = n! / (n + r)!

Answer explanation

The formula for combinations is nCr = n! / r!. This formula calculates the number of ways to invite a certain number of friends.

How many different ways can you arrange five books on a shelf?

• 60

• 120

• 720

• 240

Answer explanation

There are 5 books and each can be arranged in 5 different positions. Therefore, the total number of arrangements is 5! = 120. So, the correct answer is 120.