Do Now: Make a tree diagram that shows the number of different objects that can be created.

1
Do Now Make a tree diagram that shows the number
of different objects that can be created.

• T-shirts Sizes S, M, L and
• Type long sleeved and short sleeved

2
Academy Algebra II/Trig

• 14.1 Counting,
• 14.2 Permutations and Combinations
• HW tonight-p.978(22, 24, 26),p.986(32, 34, 36)
• Tomorrow p.986-987 (38-62 even)
• Quiz 14.1, 14.2 Friday

3
Fundamental Counting Principle

• If one event occurs m ways another event occurs
  n ways, then both events occur ways.
• You have 3 shirts, 4 pairs of pants, and 2 pairs
  of shoes. How many outfits can you create?

4
Fundamental Counting Principle

• How many different license plates are possible if
  you have 1 letter followed by 2 digits followed
  by 3 letters if letters and digits can repeat?
• How many plates are possible if letters and
  digits cannot repeat?

5
Permutations

• An ordering of n objects is a permutation of the
  objects. (Order is important)
• The number of permutations of n objects is n!.

6
Permutations

• The number of permutations of r objects taken
  from a group of n distinct objects is denoted by
  
• , n total of objects, r how many you
  are taking. can also be written as
  .

• We will use the calculator to get these answers
  from HOME screen, go to MATH menu (2nd 5) and
  select probability nPr.

7
Permutations

• 10 people are in a race.
• How many different ways can the people finish in
  the race?
• How many different ways can 3 people win 1st,
  2nd, and 3rd place?

8
Permutations

• p.981 ex 3 In how many ways can 5 people be
  lined up?

9
Permutations

• P.982 ex 5 All we know about Shannon, Patrick,
  and Ryan is that they have different birthdays.
  If we listed all the possible ways this could
  occur, how many would there be? (Assume there are
  365 days in a year.)

10
Permutations with Repetition

• The number of permutations of n objects where an
  object repeats s of times.

11
Find the number of distinguishable permutations
of the letters in the word.

• 1.) WYNES
• 2.) TALLAHASSEE
• 3.) MATAWAN

12
Combinations

• An ordering of r objects from a total of n
  objects where order is not important is a
  combination.

13
Combinations

• The number of combinations of r objects taken
  from a group of n distinct objects is denoted by
  
• , n total of objects, r how many you
  are taking.

• We will use the calculator to get these answers
  from HOME screen, go to MATH menu (2nd 5) and
  select probability nCr.

14
Combination or Permutation

• P.984 ex 8 How many different committees of 3
  people can be formed from a pool of 7 people?

15
Combination or Permutation

• P.984 ex 9 In how many ways can a committee of 2
  faculty members and 3 students be formed if 6
  faculty members and 10 students are eligible?

16
Combination or Permutation

• A club has a president and vice-president
  position. Out of 12 students, how many ways can
  students be chosen for these two positions?

17
Combination or Permutation

• P.986 41 In how many ways can a committee of 4
  students be formed from a pool of 7 students?

18
Combination or Permutation

• A relay race has a team of 4 runners who run
  different parts of the race. There are 20
  students on your track squad. In how many ways
  can the coach select students to compete on the
  relay team?

19
Combination or Permutation

• P.987 53 An urn contains 7 white balls and 3
  red balls. Three balls are selected. In how many
  ways can the 3 balls be drawn from the total of
  10 balls
• If 2 balls are white and 1 is red?
• If all 3 balls are white?
• If at least 3 ball are red?

20
Combination or Permutation

• P.987 59 A baseball team has 15 members. Four
  of the players are pitchers, and the remaining 11
  members can play any position. How many different
  teams of 9 players can be formed?

21
From a standard 52-card deck, find the number of
5-card hands that contain the cards specified.

• 1.) 5 of any card
• 2.) 5 face cards

22
From a standard 52-card deck, find the number of
5-card hands that contain the cards specified.

• 3.) 5 cards of the same color
• 4.) 1 ace and 4 cards that are not aces

23
From a standard 52-card deck, find the number of
5-card hands that contain the cards specified.

• 5.) 5 clubs or 5 spades
• 6.) at most 1 queen