Mastering Permutations

What is the formula for calculating permutations of n items taken r at a time?

• P(n, r) = n! / (n - r)!

• C(n, r) = n! / r!

• P(n, r) = n! / (n + r)!

• P(n, r) = n! * (n - r)!

Calculate the number of permutations of 5 items taken 3 at a time.

• 120

• 15

• 60

• 30

If a password consists of 4 different letters, how many different passwords can be formed?

• 14400

• 25600

• 358800

• 1200

How many ways can 6 students be arranged in a line?

• 840

• 600

• 360

• 720

A committee of 3 is to be formed from 10 people. How many different committees can be formed?

• 100

• 150

• 120

• 90

If you have 7 different books, how many ways can you arrange them on a shelf?

• 5040

• 4032

• 720

• 1000

In how many different ways can the letters of the word 'MATH' be arranged?

• 12

• 24

• 36

• 18

A race has 8 participants. How many ways can the top 3 positions be filled?

• 336

• 48

• 256

• 120

If you can choose 2 toppings from a list of 5 for a pizza, how many different combinations can you create?

• 5

• 10

• 15

• 20

Explain a real-life scenario where permutations are used in organizing events.

• Permutations are used to schedule performances in a music festival.

• Permutations are used to determine the seating arrangement for a wedding.

• Permutations are used to create a guest list for a corporate event.

• Permutations are used to select the menu items for a dinner party.