Factorials, Permutations, and Combinations

This video tutorial covers various counting problems using principles of permutations and combinations. It begins with a combination lock problem, explaining the importance of order in permutations. The tutorial then explores arranging books on a shelf, calculating pizza topping combinations, and drawing cards from a deck. It also discusses circular permutations and arranging people with specific restrictions. The video aims to enhance understanding of counting principles through practical examples.

How many possible combinations are there for a lock with 3 numbers ranging from 0 to 39?

• 100,000

• 40,000

• 64,000

• 1,000

What is the factorial of 7, which represents the number of ways to arrange 7 books on a shelf?

• 3,600

• 5,040

• 2,520

• 720

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

• n!/r!

• n!/(n-r)!

• n!

• n!/(n+r)!

What is the value of 0 factorial (0!)?

• 0

• 1

• Undefined

• 10

If you have 5 different pizza toppings, how many different pizzas can you order?

• 50

• 32

• 25

• 10

How many ways can you choose 2 toppings from 5 available options?

• 5

• 20

• 15

• 10

How many ways can you draw 4 cards from a deck of 52 cards?

• 1,000,000

• 52,000

• 500,000

• 270,725

In a circular arrangement, how many ways can 5 people sit around a table?

• 24

• 120

• 60

• 12

When arranging 5 girls and 2 boys in a row, how many total arrangements are possible?

• 1,440

• 720

• 5,040

• 2,520

If two boys must sit next to each other in a row of 7 people, how many arrangements are possible?

• 720

• 2,520

• 5,040

• 1,440