Exploring Permutations and Combinations with AND and OR

What determines the choice between permutation and combination?

• The total number of items available

• Whether order matters

• If repetition is allowed

• The number of items to choose from

How many ways can six runners advance to the second race from a group of ten?

• 720

• 120

• 5040

• 210

For winning the three prizes in the second race, why is permutation used?

• Because the order of winning matters

• Because there are only three prizes

• Because all runners have an equal chance

• Because it involves addition

How many ways can a group of three or four students be selected from fifteen?

• 1365

• 1820

• 455

• 5005

What is the total number of ways to form a non-empty group of at most three students?

• 455

• 575

• 680

• 120

How many five-card hands consist only of face cards?

• 1035

• 1287

• 792

• 1540

What is the number of five-card hands with exactly two hearts?

• 792

• 1287

• 712,842

• 1035

How many hands have at least three jacks?

• 792

• 1035

• 5005

• 4560

In the context of card games, why is combination often used?

• Because the order of cards doesn't matter

• Because all cards are unique

• Because it involves multiplication

• Because there are 52 cards in a deck

Why do the numbers in card problem solutions always add up to the total number of cards and the hand size?

• To ensure all cards are accounted for

• Because of the rules of poker

• It's a coincidence

• To make the problems easier