Page 821 - Algebra 1

Example
3
Application: Probability
An animal shelter has 20 dogs. Each month 3 of the dogs are randomly chosen to be pets-of-the-month on the website.
What is the probability that Jumbo, Fluffy, and Max will be selected?
SOLUTION
Note that the order in which the dogs are chosen does not matter, so it is a combination.
__ 20C3 = 20!
_3!(20 - 3)! = 20! = 1140
There are 1140 ways 3 dogs can be chosen, but only one way that a
3!17!
Use the formula. Substitute 20 for n and 3 for r.
Simplify.
Hint
Remember, the t_heoretical_probabilityof an event is
e outcomes total number of outcomes
# of favorabl
particular set of 3 dogs, {Jumbo, Fluffy, and Max}, can be chosen. So, the
1 probability of choosing that set is _1140 .
Lesson Practice
A teacher selects 2 students from a group of 5 students.
a. How many permutations of the 2 students are possible?
(Ex 1)
b. How many combinations of the 2 students are possible? (Ex 1)
c. To color a map, each student chooses 4 markers from a box of 8. How
(Ex 2)
many combinations are there?
d. To pick a parent committee for his class, the teacher chooses 9 parents
(Ex 2)
e. A cook has 18 possible ingredients for soup. He only uses 4 ingredients.
(Ex 3)
out of the 22 volunteers. How many combinations can the teacher make?
What is the probability he will pick beans, corn, rice, and carrots?
Practice
Distributed and Integrated
*1. Photography A photographer wants to take a picture of a group of 4 students (118) from a class of 15. How many different pictures could she take?
Calculate each combination.
*2. 11C4 3. 9C7
(118) (118)
*5. Write Explain the difference between per_mutations and combinations. (118)
4. 12C5 (118)
*6. Verify Show that 8C3 = P . (118) number of ways to order 3 items.
806 Saxon Algebra 1
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