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Practice with Counting Permutations and Combinations
Show your work or explain your thinking. There may be a few different methods that work.
1. The local pizzeria offers a choice of 2 pizzas (supreme or vegetarian), 3 sides (chips, salad, or coleslaw), and 4 drinks (juice, coke, ginger beer, or water). For dinner I decide to have 1 pizza, 1 side, and 1 drink. How many possible meals do I have to choose from?
2. How many different car plates could be made if each will display 4 letters followed by 2 numbers? Assume repetition is allowed.
3. How many different car plates could be made if each will display 4 letters followed by 2 numbers? Assume repetition is not allowed.
4. Your friend wants to perform a magic trick and asks you to draw 2 cards from a standard deck of 52. The first card you draw must be placed face down, and the second card placed face up on the table. How many ways are there of drawing the two cards?
5a. In an 18 team league, how many ways can the 8 teams for the finals be decided?
5b. In an 18 team league, how many ways can the first 4 positions be decided?
6. A child wants to draw a picture using only three different colours from a set containing twelve different colour pencils. In how many ways can the colours be chosen?
7. In the front of a building there are three doors each to be painted a different colour from twelve different available colours. How many colour arrangements for the doors are there?
Practice with Independent or Mutually Exclusive Events
1. Would the amount of time a customer spends browsing online have an impact on the amount of money they spend? To put it another way, is "Shopping Time" independent of "Money Spent"? Complete the table by finding the totals.
|Shopping Time||$0 to $50 Spent||$51 to $100 Spent||$101 or More Spent||Total|
|0 to 10 Minutes||30||35||18|
|11 to 20 Minutes||22||42||20|
|21 or More Minutes||5||13||15|
2. Can you make any conclusions from these numbers? Does shopping longer make you spend more?
For the follwing problems, write probabilities as decimals rounded to 2 decimal places.
3. What is the probability that a shopper spends 0 to 10 minutes shopping?
4. What is the probability that a shopper spends over 21 minutes shopping? (Name this event A.)
5. What is the probability that a shopper spends more than $100? (Name this event B.)
6. What is the probability that a shopper 0 to 10 minutes shopping and spends more than $100?
7. What is P(A and B)?
8. What is P(A) × P(B)?
9. Based on this information, do you think that shopping time and money spent are independent?
10. What is P(A or B)?
11. Find the probability that a shopper either spends 11-20 minutes shopping, or over 21 minutes shopping.
These problems are not graded. They are only to help you practice with our math topics. Do not rush to look at answers! First ask for hints from your instructor or classmates. But if you are really ready, the answers are here.