Combinations

Question 1

A restaurant has two options for salad, four options for entree and two options for dessert. If a person must choose one of each course, how many different combinations are there for dinner?

Answer 1

2C1 x 4C1 x 2C1 = 16

Question 2

If an ice cream shop has 9 different toppings and customers must choose 3 flavours, how many different kinds of ice cream can people buy?

Answer 2

9C3 = 84

Question 3

If Sally is buying records at a yard sale, and there are 7 different records available, how many different combinations of records can she buy if she buys 3?

Answer 3

7C3 = 35

Question 4

If you are choosing a team of three people from 18 men and 22 women, how many different teams can you make with exactly 2 women?

Answer 4

22C2 x 18C1 = 231 x 18 = 4158

exactly 2 women means exactly 1 man on the team

Question 5

If you are choosing a team of three people from 18 men and 22 women, what is the probability you make a team with exactly 1 woman?

Answer 5

probability = (# of teams with 1 woman) / (# of teams with no restriction, so choosing 3 people from 18 men +22 women)
= (22C1 x 18 C2) / (40C3) = 0.34 or 34%

Question 6

For a chilli recipe, you have to choose:

• 2 types of cheese from 4 total kinds
• 3 types of meat from 5 total kinds
• a yellow onion or a white onion
• kidney beans or black beans

How many different kinds of chilli are possible?

Answer 6

4C2 x 5C3 x 2C1 x 2C1 = 240 different recipes

Question 7

You are choosing a group of 2 from 10 people. What is the probability that you choose Todd and Mary?

Answer 7

probability = (# with Todd and Mary) / (# of teams with no restriction)
= (1C1 x 1C1) / (10C2) = 1/45 = 0.02 or 2%

Question 8

There are 5 red marbles and 8 black marbles in a bag. What is the probability of picking a red marble and then a black marble (assume no replacement between picks)?

Answer 8

(5/13) x (8/12) = 0.26 or 26% or 10/39

Question 9

There are 10 healthy flies and 7 unhealthy flies in a cage. If you pick 3 flies randomly, what is the probability of picking 3 healthy flies?

Answer 9

probability = (# with healthy flies) / (# of teams with no restriction)
= (10C3)/ (17C3) = 120/680 = 0.18 or 18%

Question 10

There are 5 red marbles and 8 black marbles in a bag. What is the probability of picking a red marble and then a black marble (assume replacement between picks)?

Answer 10

(5/13) x (8/13) = 0.24 or 24%