Permutation
What is a Permutation?
Permutation is an arrangement of all or part of a set of objects with proper regard to order.
Evaluate 8C5.
56
An action where the result is uncertain.
Experiment
What is the difference between a Permutation and a Combination?
A permutation is an arrangement of items in which order matters.
A combination is a selection of items in which order does not matter.
What are the three methods of determining permutation?
Systematic Listing
Tree Diagram
Fundamental Counting Principle
What is the formula used in determining combinations of n distinct objects taken r at a time?
nCr=n!/(n-r)!r!
Events that cannot happen at the same time.
Mutually Exclusive Events
What is Probability?
Probability is a field of mathematics that deals with chances.
How likely something is to happen.
The branch of mathematics concerned with analyzing the chance that a particular event will occur.
Find the numbers of different ways of placing 10 balls in a row given that 4 are red, 3 are green, 2 are yellow, and one blue.
12, 600 different ways
In how many ways can a teacher choose 5 of her 36 students to join a contest?
376, 992 ways
A spinner, numbered 1–8, is spun once. What is the probability of spinning an even number?
4/8 = 0.5 = 50%
CONGRATULATIONS
Bonus Points!
In how many ways can the letters in the word HAPPY be arranged where the P’s are together?
24 ways
A team of 5 people is to be selected from a group of 12. How many different teams can be formed?
792 different teams
A card is drawn at random from a 52-deck of card. What is the probability of getting a red card or a spade?
26/52 + 13/52 = 39/52 = 3/4 = 0.75 = 75%
Two dice are rolled. What is the probability that both dice turn up the same number?
6/36 = 0.1667 = 16.67%
Camy, Yvanne, Mark, Arlyn, and Roger are sitting in the stands at a concert together. How many ways can they be seated?
5! = 120 ways
CONGRATULATIONS!
Bonus Points!
A card is drawn at random from a 52-deck of card. What is the probability of getting a number card or a 4?
36/52 + 4/52 - 4/52 = 36/52 = 0.6923 = 69.23%
Two dice are rolled. What is the probability that the sum is greater than 5?
26/36 = 0.7222 = 72.22%