Exploring Permutations and Combinations

The video tutorial introduces the probability unit, focusing on permutations and combinations. It explains independent and dependent events, the basic counting principle, and factorial notation. The tutorial covers permutations, where order matters, and combinations, where order doesn't matter, using examples and calculator instructions.

What is an independent event in probability?

• An event that always occurs

• An event that has no influence on the outcome of another event

• An event that is impossible to occur

• An event that influences the outcome of another event

How many outfits can you make with 5 shirts and 3 pairs of jeans?

• 8 outfits

• 15 outfits

• 20 outfits

• 10 outfits

What does 5 factorial (5!) represent?

• 5 + 4 + 3 + 2 + 1

• 5 / 4 / 3 / 2 / 1

• 5 - 4 - 3 - 2 - 1

• 5 * 4 * 3 * 2 * 1

What is the formula for permutations?

• nPr = n! - (n-r)!

• nPr = n! / (n-r)!

• nPr = n! * (n-r)!

• nPr = n! + (n-r)!

How many ways can 32 soccer teams finish first, second, and third in the World Cup?

• 4960 ways

• 120 ways

• 362880 ways

• Not enough information

What is the formula for combinations?

• nCr = n! - r!(n-r)!

• nCr = n! + r!(n-r)!

• nCr = n! * r!(n-r)!

• nCr = n! / r!(n-r)!

How many different combinations can be made from 15 tracks on a CD, choosing 5?

• 5005 combinations

• 3003 combinations

• 455 combinations

• 252 combinations

How many ways can three cars be selected from eight cars and four trucks from eleven trucks?

• 1540 ways

• 792 ways

• 18480 ways

• 495 ways

If repetition is allowed, how many five-digit combinations can be made?

• 10000 combinations

• 100000 combinations

• 3125 combinations

• None of the above

How many five-card hands are possible with no face cards from a standard deck?

• 658008 combinations

• 2598960 combinations

• 1081 combinations

• Combinations cannot be calculated with given information