10.1 Apply the Counting Principle and Permutations

Essential Question: How do you determine the number of
distinguishable permutations in the letters of a word?
Demonstrated in writing in practice problems.
ο‚— Permutation- an ordering of n objects
ο‚— Factorial- represented by !
ο‚— 𝑛! = 1 βˆ™ 2 βˆ™ 3 βˆ™ 4 βˆ™ 5 βˆ™ β‹― βˆ™ (𝑛 βˆ’ 1) βˆ™ 𝑛
ο‚— 5! = 1 βˆ™ 2 βˆ™ 3 βˆ™ 4 βˆ™ 5 = 120
ο‚— 7! = 1 βˆ™ 2 βˆ™ 3 βˆ™ 4 βˆ™ 5 βˆ™ 6 βˆ™ 7 = 5040
EQ: How do you determine the number of distinguishable permutations in the letters of a word?
Demonstrated in writing in practice problems.
ο‚— Two Events If one event can occur in m ways and
another event can occur in n ways, then the number of
ways that both events can occur is m βˆ™ n.
ο‚— Three or More Events The fundamental counting
principle can be extended to three or more events. For
example, if three events occur in m, n, and p ways,
then the number of ways that all three events can
occur is m βˆ™ n βˆ™ p.
EQ: How do you determine the number of distinguishable permutations in the letters of a word?
Demonstrated in writing in practice problems.
EQ: How do you determine the number of distinguishable permutations in the letters of a word?
Demonstrated in writing in practice problems.
EQ: How do you determine the number of distinguishable permutations in the letters of a word?
Demonstrated in writing in practice problems.
EQ: How do you determine the number of distinguishable permutations in the letters of a word?
Demonstrated in writing in practice problems.
ο‚— In how many different ways can the baseball teams
finish the competition?
ο‚— In how many different ways can 3 of the baseball teams
finish first, second, and third?
EQ: How do you determine the number of distinguishable permutations in the letters of a word?
Demonstrated in writing in practice problems.
ο‚— The number of permutations of r
objects taken from a group of n distinct
objects is denoted by nPr
ο‚— 𝒏 𝑷𝒓 =
𝒏!
π’βˆ’π’“ !
ο‚— For permutations order matters
ο‚— ABC is not the same as ACB or BAC
EQ: How do you determine the number of distinguishable permutations in the letters of a word?
Demonstrated in writing in practice problems.
EQ: How do you determine the number of distinguishable permutations in the letters of a word?
Demonstrated in writing in practice problems.
2) How many different 7 digit telephone numbers are
possible if all of the digits can be repeated?
3) In example 3, how many different ways can the teams
finish if there are 6 teams competing in the playoffs?
4) You were left a list of 9 chores to complete. In how
many orders can you complete 5 of the chores?
EQ: How do you determine the number of distinguishable permutations in the letters of a word?
Demonstrated in writing in practice problems.
ο‚— The number of distinguishable permutations of n
objects where one object is repeated s1 times, another
is repeated s2 times, and so on, is:
𝑛!
𝑠1 ! βˆ™ 𝑠2 ! βˆ™ 𝑠3 ! βˆ™ β‹― βˆ™ 𝑠𝑛 !
EQ: How do you determine the number of distinguishable permutations in the letters of a word?
Demonstrated in writing in practice problems.
EQ: How do you determine the number of distinguishable permutations in the letters of a word?
Demonstrated in writing in practice problems.
ο‚— TOMORROW
ο‚— YESTERDAY
EQ: How do you determine the number of distinguishable permutations in the letters of a word?
Demonstrated in writing in practice problems.