Lesson 4.8 Checkpoint

On Monday nights, Papa’s Pizza offers a special two-for-one deal on its medium two-topping pizzas. All pizzas come with sauce and cheese. The customer can choose any 2 of Papa’s 25 toppings to complete the order. How many different possible pizzas are there, assuming that the customer must choose exactly 2 different toppings? (LT 4.8.1 #1)

• 300

• 50

• 600

• 1.55 x 10²⁵

A standard deck has 52 playing cards. Suppose you shuffle the deck well and deal out 5 cards. How many different possible 5-card hands are there? (LT 4.8.1 #2)

• 2598960

• 311875200

• 260

• 120

Almost everyone has one—a drawer that holds miscellaneous batteries of all sizes. Suppose that your drawer contains 8 AAA batteries but only 6 of them are good. You have to choose 4 for your graphing calculator. If you randomly select 4 batteries, what is the probability that all 4 of them will work? Use combinations to help answer this question. (LT 4.8.2 #1)

• 0.2143

• 1.875

• 0.75

In the game of Scrabble, each player begins by drawing 7 tiles from a bag initially containing 100 tiles. There are 42 vowels, 56 consonants, and 2 blank tiles in the bag. Suppose you are playing Scrabble and get to go first. If you randomly select 7 tiles from the bag, what’s the probability that all of them are vowels? Use combinations to help answer this question. (LT 4.8.2 #2)

• 26978328

• 16007560800

• 0.0017

• 0.42

At a university’s annual picnic, 18 students in the mathematics/statistics department decide to play a softball game. Twelve of the 18 students are math majors and 6 are statistics majors. To divide into two teams of 9, one of the professors put all the players’ names into a hat and drew out 9 players to form team Fisher, with the remaining 9 players forming team Newton. The players were surprised when all of the statistics majors ended up on team Fisher. Find the number of ways in which a random selection of 9 students for team Fisher would result in all 6 statistics majors (and 3 math majors) being selected. (LT 4.8.3 #1)

• 220

• 1320

• 1

• 720

At a university’s annual picnic, 18 students in the mathematics/statistics department decide to play a softball game. Twelve of the 18 students are math majors and 6 are statistics majors. To divide into two teams of 9, one of the professors put all the players’ names into a hat and drew out 9 players to form team Fisher, with the remaining 9 players forming team Newton. The players were surprised when all of the statistics majors ended up on team Fisher. Find the probability that a random selection of 9 students for team Fisher would result in all 6 statistics majors being selected. (LT 4.8.3 #2)

• 220

• 48620

• 221

• 0.0045