12.2 Combinations Homework
1.) How many starting teams volleyball teams of 6 members can be formed
from a bench of 12 talented players ?
2.) Students are required to answer any eight out of ten questions
on a certain test. How many different combinations of eight questions
can a student choose to answer ?
3.) In the Colorado state lotto game, there are 42 numbers. Players choose
any 6 different numbers. Then the state selects 6 different numbers at
random. The winning tickets (for the grand prize) are those on which the
player’s 6 numbers match the state’s six numbers. From 42 numbers, how
many groups of 6 are possible?
4.) A biology class is preparing for its final exam. From a class of 22 girls
and 16 boys, how many study groups of 2 girls and 3 boys can be formed ?
5.) You are taking a vacation. You can visit as many as five different cities
and seven different attractions.
a.) Suppose you want to visit exactly three different cities and four
different attractions. How many different trips are possible ?
b.) Suppose you want to visit at least 8 locations (cities or attractions).
How many different types of trips are possible ?
6.) In a standard deck of 52 playing cards, how many 5-card hands
are possible that contain a full house, that is 3 of one kind
and 2 of a different kind (for example, 3 jacks & 2 aces)
12.2 Combinations Homework
7.) In a standard deck of 52 playing cards, how many 5-card hands
are possible that contain 5 cards of the same suit ?
8.) A restaurant offers 6 salad toppings. On a deluxe salad, you can have up
to four toppings. How many different combinations of toppings can you
have ?
Expand the power of the binomial.
10.)
( x − 1) 7
11.)
( x + 2) 6
12.)
( x − 4 y) 4