How many subsets does a set with 12 elements have?

How many ways can a president, a vice-president, a secretary-treasurer, and three Student Senate representatives be selected from a class of thirty people? You may assume these will be six different people.

Define set .

How many four-element subsets of include at least three even numbers?

We want to create a three-character-long password using only the twenty-six letters from the English alphabet. How many different passwords can be created?

A college cafeteria offers sizes of pizza - small, medium, and large. With a small pizza, up to one topping is included without additional charge; for a medium or large, up to two toppings are included without additional charge. The cafeteria allows a double topping (i.e. double mushrooms) to count as two toppings.

The cafeteria offers three meat toppings - pepperoni, beef, and sausage. If the cafeteria offers other toppings, then how many ways can someone order a pizza -choosing a size and up to the maximum number of toppings- without having to pay extra?

What is the number of possible 4 letter code words that can be made from the alphabet, when all 4 letters must be different?

We have four keys and are asked to open four locks with those keys. Each key only opens one lock; however, we don't know which key opens which lock. At most, how many attempts must we make before we can be sure to have all locks opened?

In how many ways can the letters , , , , and be arranged to form a six-letter combination?

A pizza parlor is offering a five-topping large pizza for $14.59. The toppings must be different, and they must include two meats and two vegetables; the fifth can be either. The meat toppings are pepperoni, beef, and sausage; the vegetable toppings are mushrooms, olives, onions, and green peppers.

How many possible ways can the toppings be chosen?

Fred shuffles a deck of 52 cards. He then draws 1 card and keeps it. Then he draws a 2nd card. Then he puts it back into the deck and shuffles again. Fred then draws a 3rd card and keeps it

What's the probability that the 2nd and 3rd cards are the same?