Math 103 - Cooley
Statistics for Teachers
OCC
Activity #19 – Combinations
California State Content Standard - Statistics, Data Analysis, and Probability
N/A
Combination Formula
The number of possible combinations (unordered or no arrangement) of r objects from a collection of n
objects is given by the formula:
n
n!
nCr = C( n , r ) = 
 r  = (n  r )!r!
 
 Exercises:
1)
In how many ways can a sorority of 20 members select three members to serve on a committee?
2)
You are going to draw 5 cards from a standard deck of 52 cards. How many different 5 card hands
are possible?
3)
A boss has 8 employees and 5 are chosen to give a presentation. How many different ways can the
boss choose the presenters if the order of the presenters is not important?
4)
Marty wants to purchase six different CDs but only has enough money to purchase four. In how
many ways can he select four of the six CDs for purchase?
5)
A textbook search committee is considering seven books for possible adoption. The committee has
decided to select three of the seven for further consideration. In how many ways can they do so?
6)
At a medical research center an experimental drug is to be given to 12 people, 6 men and 6 women.
If 10 men and 9 women have volunteered to be given the drug, in how many ways can the researcher
choose the 12 people to be given the drug?
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 Exercises:
7)
There are 12 boys and 14 girls in Mrs. Payne's math class. Find the number of ways Mrs. Payne can
select a team of 3 students from the class to work on a group project. The team must consist of 1 girl
and 2 boys.
8)
Five freshman, 4 sophomores, and 2 juniors are present at a meeting of students. In how many ways can a
six-member committee of three freshmen, two sophomores, and one junior be formed?
9)
Eight students names will be drawn at random from a hat containing 14 freshmen names, 15 sophomore
names, 8 junior names, and 10 senior names.
10)
a)
How many different draws of 8 names are there overall?
b)
How many different draws of 8 names would contain only juniors?
c)
How many different draws of 8 names would contain exactly 4 juniors and 4 seniors?
In 1988, the California Lottery was initiated. There were 49 lotto balls, each numbered from 1 to 49.
In order to play, you must choose 6 numbers.
a) In how many ways can someone choose 6 numbers from the 49?
b) A player chooses 6 numbers. In how many ways can someone hit all 6 numbers?
c) A player chooses 6 numbers. In how many ways can someone hit exactly 5 numbers?
d) A player chooses 6 numbers. In how many ways can someone hit none of the 6 numbers?
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