Deck Of Cards Lab 1
Counting the Number of Ways An Event Can Occur

    Before you can complete this lab, you must know the cards in a deck of playing cards.

    Click on the picture of the playing cards to see what they are called. Then you may answer the questions below.

    Below you complete a question, mouseover the "Answer" button to read the answer.

1. If you use just the aces, in how many ways can you get a heart?
2. If you use just the hearts, in how many ways can you get a ace?
3. Considering just the black cards, in how many ways can you get a heart?
4. If you use just the clubs, in how many ways can you get a face card?
5. Considering just the aces, in how many ways can you get a ace?

Given a regular deck of cards,

1. In how many ways can you get a heart?
2. In how many ways can you ?
3. In how many ways can you get a ace?
4. In how many ways can you get a face card?
5. In how many ways can you get a black card?
6. In how many ways can you get the King of Clubs?
7. In how many ways can you get a card that is an ace and at the same time a club?
8. In how many ways can you get a card that is an ace or is a club?

      Without replacement means you take a card, then, without returning it to the deck take a second card.

1. If you use just the black cards, in how many ways can you get a ace then a two?
2. Considering just the black cards, in how many ways can you get a face card then another face card?
3. Considering the full deck, in how many ways can you get a face card then another face card?
4. If you use just the clubs, in how many ways can you get a face card then another face card?
5. Considering the entire deck, in how many ways can you get a deuce then a face card?
6. Considering the full deck, in how many ways can you get a heart then a second heart?

      With replacement means you take a card, then, return it to the deck, then take a second card.

1. If you use just the black cards, in how many ways can you get a ace then a two?
2. Considering just the black cards, in how many ways can you get a face card then another face card?
3. Considering the full deck, in how many ways can you get a face card then another face card?
4. If you use just the clubs, in how many ways can you get a face card then another face card?
5. Considering the entire deck, in how many ways can you get a deuce then a face card?
6. Considering the full deck, in how many ways can you get a heart then a second heart?

1. In how many ways can you draw 3 cards without replacement from the face cards?
2. In how many ways can you draw 3 cards with replacement from the face cards?
3. In how many ways can you draw 5 cards without replacement from the deck of red cards?
4. In how many ways can you draw 2 cards from the full deck without replacement?
5. In how many ways can you draw all 52 cards from the deck without replacement?

      All the problems on this page deal with ordered lists and the next page deals with computing probability involving ordered lists.

      There is an easy way to compute the numbers of ways to make an ordered list. It is the permutation formula (shown below). To learn of this, visit page Number of Ways to Make An Ordered List.

	n!		(number of ordered lists given n things)
Pn,x =		=
	(n-x)!		(shorten the list so only x things are used)