Mastering Combinations and Permutations

What is the number of permutations of 5 objects taken 3 at a time?

• 120

• 15

• 30

• 60

Calculate the number of combinations of 10 students taken 4 at a time.

• 120

• 45

• 210

• 56

If a pizza shop offers 3 types of crust and 5 toppings, how many different pizzas can be made if you choose 1 crust and 2 toppings?

• 30

• 20

• 15

• 25

Differentiate between permutations and combinations with an example.

• Permutations: Order does not matter; Combinations: Order matters.

• Permutations: Only for large sets; Combinations: For small sets.

• Permutations: Used in statistics; Combinations: Used in algebra.

• Permutations: Order matters; Combinations: Order does not matter.

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

• 6

• 24

• 18

• 12

A committee of 3 is to be formed from a group of 8 people. How many different committees can be formed?

• 24

• 36

• 56

• 84

If you have 7 different books and want to arrange 4 of them on a shelf, how many arrangements are possible?

• 840

• 28

• 210

• 5040

In how many ways can you select 2 fruits from a basket containing 5 different fruits?

• 15

• 5

• 10

• 20

A password consists of 3 letters followed by 2 digits. How many different passwords can be created if letters and digits can be repeated?

• 10000000

• 5000000

• 17576000

• 123456

Explain a real-world scenario where you would use combinations instead of permutations.

• Selecting 3 flavors for an ice cream cone from 10 available flavors.

• Choosing 3 members from a group of 10 people.

• Arranging 3 books on a shelf from a collection of 10 books.

• Choosing 3 routes for a trip from 10 possible routes.