Math 12 – Combinatorics Worksheet #4 – Combinations
Complete the following questions on a separate piece of paper, remember to show work.
1.) Pete’s Perfect Pizza Company has 9 choices of topping available.
a) How many different 2-topping pizzas can be made?
b) How many different 3-topping pizzas can be made?
2.) There are seven gifts to be distributed to 10 children. How many ways can this be done if no
child is to receive more than one gift?
3.) McMath’s basketball team have a starting line-up consisting of 5 players, if there are 13
players to choose from, how many different selections are possible for the starting line-up?
4.) McMath has a twelve-member student council. A four member sub-committee is to be
selected to organize school dances,
a) How many different sub-committees are possible?
b) How many different sub-committees are possible if council president must be a member?
5.) McMath basketball team has 5 guards and 7 forwards,
a) How many different ways can a line-up can be selected with 2 guards and 3 forwards?
b) How many different ways can a line-up be selected if a star player, who plays guard, must
being in the line up?
6.) Four students are chosen from a class of 20 to be group captains.
a) How many ways are there to do this?
b) Each captain chooses four other team members, how many ways can this be done?
7.) Twelve face cards are removed from a deck of 52 cards. From the face cards, three card
hands are dealt. Determine the number of distinct three card hands that are possible which
include:
a) no restrictions
b) 3 kings
c) 1 queen and 2 kings
d) only 1 jack
8.) Consider a standard deck of 52 cards. Determine the number of distinct six card hands that
are possible which include:
a) no restrictions
b) only clubs
c) 2 clubs and 4 diamonds
d) no sevens
e) 4 tens
f) only 1 jack and 4 queens
9.) A group of 4 committee is chosen from student council to organize a food drive, there are 5
male and 7 female members on student council. How many possible groups can be formed:
a) consisting of 2 male and 2 female
b) consisting of at least one women
10.) Consider a standard deck of 52 cards. How many different four card hands have:
a) at least one red card?
b) at least 2 kings?
c) two pairs
d) at most 2 clubs?
11.) An all-night showing at a movie theatre is to consist of 5 movies. There are 14 different
movies available, 10 disaster movies and 4 horror movies. How many possible schedules
include:
a) at least one horror movie?
b) at least four disaster movies?
c) both movies with titles “Airport Disaster” and “Halloween Horror”?
12.) How many people are there in a class in which there are 20 ways to select a committee of
three people?
13.) Solve for n.
a) nC3 = 84
b) 11Cn = 330 (2 answers)
14.) Simplify the expression, n-1Cr-1 + n-1Cr
c) nC7 = n+1C8