Hawkes Learning, Beginning Statistics
Math 104, 4.5 Combining Probability and
Counting Techniques | Questions &
Answers (100% VERIFIED)
Paolo's Pizzeria offers 6 types of crust, 10 toppings, and 5 kinds of cheese for the mega
calzone. How many different mega calzones can be made if a mega calzone contain 3 different toppings and 2 different cheeses? - ANSWER - Toppings: 10 C 3= 120
Cheese: 5 C 2= 10
Crust 6 C 1= 6
120*10*6=7200 different mega calzones
An English teacher needs to pick 11 books to put on his reading list for he next school year. He has narrowed down his choices to 12 novels, 8 plays, and 12 nonfiction books.
If he wants to include 5 novels, 4 plays, and 2 nonfiction books, how many ways can he choose the books to put on the list? - ANSWER - Novels: 12 C 5= 792
Plays: 8 C 4=70
Nonfiction books: 12 C 2= 66
792*70*66= 3659040 ways
At the grocery store, Michael has narrowed down his selections to 7 vegetables, 3 fruits,
4 cheeses, and 3 whole grain breads. He wants to use the Express Lane, so he can only buy 15 items. In how many ways can he choose which 15 items to buy if he wants all 4 cheeses? - ANSWER - 7 veggies + 3 fruits + 3 breads = 13 items
Cheeses: 4 C 4= 1
15 items - 4 cheeses = 11 items
13 C 11= 78 ways
How many ways can a person toss a coin 14 times so that the number of heads is between 6 and 9 inclusive? - ANSWER - 14 C 6= 3003
14 C 7= 3432
14 C 8= 3003
14 C 9= 2002
3003 + 3432 + 3003 + 2002= 11440 ways
How many different teams of 3 children can be chosen from a group of 14 girls and 13 boys if each team must have at least one boy on it? - ANSWER - 13 C 1 (=13) * 14 C 2 (=19) =1183
13 C 2 (=78) * 14 C 1 (=14) =1092
13 C 3 (=286) * 14 C 0 (=1) =286
1183 + 1092 + 286= 2561 different teams
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