734 CHAPTER 11 Probability Example 2 Book Selection In your American History class, you are assigned to read any 3 books, in any order, from a list of 8 books. In how many ways can you select 3 of the 8 books to read? Solution This problem is a combination problem because the order in which the three books are selected and read does not matter. C 8! (8 3)!3! 8! 5!3! 8 7 6 5 4 3 2 1 5 4 3 2 1 3 2 1 56 8 3 = − = = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = There are 56 different ways that you can select 3 of the 8 books to read. 7 Now try Exercise 23 Timely Tip When evaluating combinations, the following are true for any positive integer, n. C 1 n 0 = C n n 1 = C n n n 1 = − C 1 n n = Also, remember that 0! 1 = and 1! 1. = TECHNOLOGY TIP Evaluating Combinations Most scientific and all graphing calculators can evaluate combinations. While the commands on these calculators may vary depending on the model, look for a key or function that has the notation nCr . If you cannot locate this key or function, conduct an Internet search with your calculator model and the word combination . For example, if you search for “Casio FX-82MS combination” you will be directed to several websites including online videos that can assist you. Also, there are many apps for smartphones and tablets that can be used to calculate combinations. To evaluate C8 3 on a TI-84 Plus calculator, enter the number 8. Then press the MATH key. Use the right arrow key to scroll to PRB, and then scroll to nCr. Press the ENTER key. Next, press 3. Press the ENTER key again. The calculator will display 56, which agrees with our answer in Example 2. The screenshots below show the calculation depending on the version of the TI-84 Plus. Example 3 Brain Bowl Decisions Isaac is the faculty advisor for the Brain Bowl Team at Northeast Texas Community College. For an upcoming tournament, Isaac selects a team of 4 players from 6 eligible students. a) How many different teams of four players are possible? b) After the tournament, Isaac takes the team out for pizza. They order an extralarge pizza and must choose 3 toppings from a list of 11 toppings. How many different three-topping pizzas are possible?
RkJQdWJsaXNoZXIy NjM5ODQ=