Page 772 - Algebra 1

b. A total of 6 classes are competing to see who can collect the most recyclable materials. In how many different ways can the classes finish in first and second place?
SOLUTION
This is_a permutation of 6 things taken 2 at a time. nPr = n! Write the formula.
Simplify.
Writethefactorsof6!and4!.Thensimplify. Multiply.
(n - r)! __
Math Reasoning
Generalize Another way to think about permutations of n Pr
is to multiply the first
r numbers of n! . So 5P3 would be 5 · 4 · 3 = 60. Explain how to find 7P2 and then find its value.
6P2 = 6! = 6! (6 - 2)! 4!
= 6·5·4·3·2·1 =6·5 __
= 30
4·3·2·1
Example
4
Application: Uniform Numbers
The 15 members of a softball team have uniform numbers 1 through 15. They are introduced randomly at a pep rally. What is the probability that the first 4 players introduced will have uniform numbers 1, 2, 3, and 4 in that order?
SOLUTION
Of the possible permutations only 1, 2, 3, 4 is favorable. The probability is represented by:
numberof waystochoose1,2,3,4 = _____
_
1 __
1 number of ways to choose 4 numbers 15P4
=
1 15 · 14 · 13 · 12 32,760
=
Lesson Practice
a.
(Ex 1)
b.
(Ex 1)
c.
(Ex 2)
d.
(Ex 2)
e.
(Ex 3)
f.
(Ex 3)
While trying to schedule a flight for vacation, you are given two choices for departure and four choices for the return flight. How many ways can you schedule your flights for the trip?
A video game character has 6 choices each for hair color, face, attitude, and outfit as well as a choice of male or female. How many different characters are possible?
Find 5!.
_ Find 6!.
You are selecting your class schedule for the school year. If there are 7 periods and each of the seven classes are taught each period, how many possible ways are there for your schedule to be determined?
There are 10 people in the Activities Club. In how many different ways can a president, vice-president and treasurer be selected from the club members?
3!
Lesson 111 757