Mastering Factorials: Arrangements & Combinations Challenge

A group of 5 friends wants to take a photo. In how many different ways can they arrange themselves in a line?

• 24

• 120

• 60

• 30

A teacher has 8 different books and wants to select 3 to take to a conference. How many different combinations of books can she choose?

• 24

• 56

• 36

• 84

In a race with 10 participants, how many ways can the top 3 finishers be arranged on the podium?

• 360

• 1000

• 540

• 720

A pizza shop offers 4 different toppings. If a customer wants to choose 2 toppings for their pizza, how many different combinations can they make?

• 6

• 10

• 8

• 4

A committee of 4 members is to be formed from a group of 10 people. How many different ways can the committee be formed?

• 300

• 210

• 180

• 150

A password consists of 3 letters followed by 2 digits. How many different passwords can be created if letters can be repeated but digits cannot?

• 160000

• 180000

• 175000

• 175560

In how many ways can 6 different colored balls be arranged in a row?

• 720

• 840

• 360

• 600

A school is organizing a talent show with 5 acts. In how many different orders can the acts be performed?

• 120

• 30

• 240

• 60

A student needs to choose 3 out of 7 available electives. How many different combinations of electives can the student select?

• 35

• 42

• 21

• 28

A chef is preparing a special dish that requires 4 out of 10 available ingredients. How many different combinations of ingredients can the chef choose?

• 120

• 56

• 210

• 45