A standard piano keyboard has 88 different keys. Find the probability that a cat, jumping on 3 keys in sequence and at random (possibly with repetition), will strike the first three notes of Beethoven's Fifth Symphony. (Leave your answer as a formula.) Consider a bag containing four red marbles, two green ones, one transparent one, four yellow ones, and three orange ones. How many possible sets of five marbles are there in which none of them are red or green?

Assume that you have a 52-card deck at hand and you are planning to draw 5 cards from the deck. How many possible combinations are there with 5 cards?

A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had  5  answer choices –  a ,  b ,  c ,  d ,  e  – and only one correct answer. What is the probability that he answered both of the problems correctly? Do not round your answer. (If necessary, consult a list of formulas.)

If you have 33 regular decks of 52 cards, how many hands of 33 cards can be made, where all cards are of the same suit?

In a certain card game, for every 4 blue cards, there are 3 yellow cards. There are a total of 84 blue and yellow cards in the game.

How many two pairs (two cards with the same face, two more cards with the same face, and another card) are possible in 5 card poker?

A teacher will randomly award three students with extra credit. How many possible ways can the teacher pick these three students from a class of 20 students?

If you pick 4 cards without replacement from a standard deck of 52 cards, how many different combinations are possible?

If they decide to purposely choose 2 of the 22 available dogs rather than randomly choosing any 2, how many combinations of 2 dogs are possible?

Assume that you have a 52-card deck at hand and you are planning to draw 7 cards from the deck. How many possible combinations are there with 7 cards?