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Probability, Perms and Combs: Weighting: 33%, (about 1314 questions)
Diploma Review Permutations and Combinations
Fundamental Counting Principle
Example 1:A dinner consists of appetizers, entree, and dessert.How many meals exist?
Appetizers: Bread, Salad, Chicken WingsEntrees: Pasta, Chicken, Fish, SteakDessets: Pie, Sundae, Cupcake
Fundamental Counting Graphic OrganizerPrinciple
The number of three digit or four digit even numbers that can be formed from the numbers 2, 3, 5, 6, and 7 is
A. 72B. 120C. 144D. 5040
Example 2
Factorials
Factorials are used when arranging all members of a group.
Example 1How many ways can 8 people line up at the cafeteria?
Solve for n in the equation
Example 2
How many arrangements of the Letters in the word TRAINS if:
a) No other restrictions
b) vowels are at the end
c) vowels are not together
Example 3
Example 4
A grocery store manager is trying to decide how to arrange the following items in the produce isle.
The items can be arranged in any order, but he does not want the pumpkins and watermelons together. If this is the only restriction, the number of possible arrangements is...
Avacados, pumpkins, eggplant, squash, watermelon.
A. 5B. 45C. 72D. 120
Repeated items Remember to divide out to avoid repeating arrangements.
How many arrangements of the word TOMATOESa) no other restrictions
b) vowels are together
c) Starts and ends with a T
Example 5
The number of arrangements of the word BANANA is
A. 60B. 144C. 120D.720
Example 6
On a 8 question multiple choice test, how many keys existif there are 2 A's, 3 B's, 1 C, and 2 D's?
Example 7
Pathways
How many different routes could be used to get from point A to point B if you must move only down and to the right?
A
B
A
B
A
B
Permutations
Permutationsorder matterscodes, passwords, batting order,players in position, president,
secretary,treasurerarrangements
In the 100 m race at the Olympics, there are 8 lanes.In how many ways can gold, silver, and bronze beawarded?
Example 1
A committee has 9 members. In how many ways can a president, secretary, and treasurer be selected?
Example 2
A cast has 2 female and 3 male leads. There are 8 females and 9 males auditioning.
In how any ways can the cast be chosen?
Example 3
Combinations
Combinationsorder does not mattercommittees, pizza topppings, round, robin tournaments, handshakeschosen or selected
A committee has 8 students and 5 teachers. How many ways can a subcommittee of 3 be chosen if:a) no other restrictions
b) must have more teachers than students
c) If the principal and student council president must be on the committee
d) there are at least 2 students
Example 1
Example 2The number of committees consisting of 4 men and 5 women that can be formed from 10 men and 13 women is
A.
B.
C.
D.
a 7 digit phone number
the number of 2 topping pizzas
your 10 digit Alberta Ed number
number of games in a round robin tournament
Example 3Classify as Permuation or combination
"This should be called a permutation lock"
A committee of 4 girls and 3 boysis to be chosen from 9 girls and 7 boys.
The total number of different committees can be expressedas
The value of x, w, r, and m are
x: ________ w: ________
r: ________ m: ________
Example 4
There are 15 distinguishable possibilities when 2 people are selected to be on a committee of 2 from n people. Find n
Example 5
Solve for x
Example 6
Probability
Example 1Determine the probability that the letters from the word SMILES are drawn in that order.
Example 2A committee has 4 females and 6 males.Determine the probability that a group of 4 chosen at random, will consist of 2 males and 2 females.
