FCP, Perm/Combo, Multiplication Rule
Impossible
0% chance that the desired outcome will occur.
4/ 8 = 1/2
1 red marble, 3 green, 4 blue. what is the probability of not picking blue?
3/8
1 red marble, 3 green, 4 blue. what is the probability of picking a green?
0
1 red marble, 3 green, 4 blue. what is the probability of picking a yellow?
A group of 25 people are going to run a race. The top 8 finishers advance to the finals.
1,081,575
A table of 5 students has 3 seniors and 2 juniors. The teacher is going to pick 2 students at random from this group to present homework solutions. Find the probability that both students selected are juniors.
1/10
Gary has a deck of 52 cards. He wants to know the probability of drawing the jack of spades and then drawing the two of hearts from the deck without replacing either card. What's the probability of this event?
1/2652
Jessie has a deck of 52 regular playing cards and a bag of six marbles. In the bag, there are two blue marbles, three green marbles, and one white marble. What is the probability of Jessie drawing an ace from the deck of cards and a blue marble from the bag?
1/39
In a class of 10, there are 2 students who forgot their lunch. If the teacher chooses 2 students, what is the probability that both of them forgot their lunch?
1/45
Lisa has a two-sided coin with heads and tails. She also has a spinner with four colors: green, blue, red, and yellow. What is the probability of Lisa flipping the coin and getting heads and spinning the spinner to land on green?
1/8
Certain
100% chance that the desired outcome will occur.
There are 15 people who auditioned for the play. In how many ways can the two narrators be cast?
105
A leadership team is to be picked at ACGC where one teacher from each department where there are 3 math teachers, 4 English teachers, 3 science teachers, and 3 social studies teachers. How many teams are possible?
108
How many different 5-digit codes can be made using the digits 0-9 if repeats ARE allowed?
10x10x10x10x10
How many different 5-digit codes can be made using the digits 0-9 if repeats are NOT allowed?
10x9x8x7x6
A club of 20 members are electing a president, vice president, treasurer, and secretary. How many ways can the office be filled
116,280 ways
How many unique ways can you order the word YELL?
12
A bag contains 6 red jelly beans, 4 green jelly beans, and 4 blue jelly beans. If we choose a jelly bean, then another jelly bean without putting the first one back in the bag, what is the probability that the first jelly bean will be green and the second will be red?
12/91
There are 12 different blizzard options. If Karen, Joey, and Phil want to get three different kinds to share, how many ways is this possible?
1320
Carlos has homework assignments in six subjects. He only has time to do four of them
15
There are 13 different types of doughnuts at the bakery, in how many ways can you select 7 different options?
1716
There are 24 math problems on a quiz, in how many ways can you omit 3?
2024
How many unique ways can you order the word IMAGINE
2520
Alex has a bag of 30 buttons, 17 are red and 13 are blue. What is the probability that Alex will pull out two blue buttons in a row without looking?
26/145
Nathan has 34 jellybeans, in how many ways can he choose 5 to give to his friends?
278,256
How many different room choices are there if you have to choose: smoking or non-smoking 2 twin beds, 2 queen beds, 1 king bed, or 2 king beds
2x4
How many unique ways can you order the word CAREER?
30
Riley and the 8 other members of his family are going to a movie and are all sitting in the middle row. In how many orders can they sit?
362,880
Tracy wants to put her 8 figurines on the shelf. In how many ways can she order them?
40,320
In how many ways can a jazz band be made of one of each type of instrument when there are 13 trumpets, 12 trombones, 15 saxophones, and 20 percussionists?
46,800
How many different meal choices are there if you have 4 main dishes and 6 side dishes to choose from?
4x6
11/13
5 red marbles, 6 green, 2 blue. what is the probability of not picking blue?
6/13
5 red marbles, 6 green, 2 blue. what is the probability of picking green?
5/13
5 red marbles, 6 green, 2 blue. what is the probability of picking red?
There are 25 people who work in an office together. Five of these people are selected to go together to the same conference in Orlando, Florida. How many ways can they choose this team of five people to go to the conference?
53,130
How many unique ways can you order the word CAT?
6
There are 25 people who work in an office together. Five of these people are selected to attend five different conferences. The first person selected will go to a conference in Hawaii, the second will go to New York, the third will go to San Diego, the fourth will go to Atlanta, and the fifth will go to Nashville. How many such selections are possible?
6,375,600
Shawn and Alexis have 5 gender neutral names for their triples picked out. In how many ways can they name their triples when they arrive?
60
A locker combination contains the number 1-25, inclusive, and needs 2 numbers to open. How many ways can the locker open?
600 ways
Justin has 9 options for the last two periods of his daily schedule. In how many ways can he complete his schedule?
72
How many three digit locker combinations can be made from 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9?
720
How many unique ways can you order the word WONDER?
720
How many different committees of 3 people can be chosen to work on a special project from a group of 9 people?
84
Yolanda has 13 different colored pants, in how many ways can she create an outfit, if she has 14 different sweaters and 5 different pairs of boots?
910
A coach must choose how to line up his five starters from a team of 12 players. How many different ways can the coach choose the starters?
95,040
Jordyn has 4 different jackets, 4 pairs of boots, and 6 different scarfs. In how many ways can she wear her outerwear?
96
Trey has a class of 65 people. How many ways can the class officers be picked: President, Vice President, Secretary, and 2 Representatives?
991,186,560
Event
A group of outcomes
Real World Combination Examples
Card Games, Ice Cream Sundae flavors, Choosing a team in a game, sample, group, etc.
30240
Consider a group of 10 people. How many ways are there to form a line of 5 people from the group?
90
Count the number of possible levels Supposed room designer: 5 different styles 6 color schemes 3 different luxury levels
Outcome
The final result after all events are chosen
1037836800
Thirteen people on a softball team show up for a game. How many ways are there to assign the 10 positions by selecting players from the 13 people who show up?
Without Replacement
This a key word to identify dependent events
With Replacement
This a key word to identify independent events
Order does not matter...
for combinations
Order matters...
for permutations
the 1st, 2nd, and 3rd place finishers in a race with 10 participants
permutation
Fundamental Counting Principle
the total number of possible outcomes by multiplying together the possible outcomes for each event. (m*n outcomes for the two events together)
Permutations
ways in which a given number of elements can be rearranged from a set
Combinations
ways in which a given number of elements can be selected from a set, without regard to order
0/8 = 0
what is the probability of landing on 9?
5/8
what is the probability of landing on an even number or 3?
8/8 = 1
what is the probability of landing on an odd or even number?
How many different groups of 3 can be formed in a class of 15 students?
₁₅C₃
How many different seating charts can be made for a class of 15 students?
₁₅P₁₅
How many ways to pick a manager, clerk, and scribe from a class of 15 students?
₁₅P₃
How many ways to rearrange the letters in CAT?
₃P₃
How many ways to rearrange the letters in GROUP?
₅P₅
How many ways to choose a committee of 3 people from 8?
₈C₃
How many ways to pick 5 CDs from a set of 8?
₈C₅
How many ways to award 1st, 2nd, and 3rd place in a race of 8 people?
₈P₃
How many ways to arrange a playlist of 5 songs from 8 songs total?
₈P₅
How many ways to arrange 8 people in a line?
₈P₈
How many ways to pick 5 types of fruit out of 9 total to serve in a fruit salad?
₉C₅
How many ways to stack 5 different colored blocks out of 9 total to make a tower?
₉P₅
How many different ways to arrange 9 different books on a shelf?
₉P₉
3628800
Suppose that a saleswoman has to visit eleven different cities. She must begin her trip in a specified city, but she can visit the other ten cities in any order she wishes. How many possible orders can the saleswoman use when visiting these cities?
choosing 2 vegetables from a menu that offers 6 vegetable choice
combination
Theoretical Probability
Probability where only the theory is tabulated.
970200
How many ways are there to select a first-prize winner, a second-prize winner, and a third-prize winner from 100 different people who have entered a contest?
210
In how many ways can we arrange three students from a group of seven students to stand in line for a picture?
Real World Permutation Examples
Locker Combinations, Word Spelling, Seat Arrangements, Computer Codes, schedule, etc.
Factorial
Multiplying a series of descending natural numbers.
Dependent Events
Outcome of one affects the probability of outcome of the other
Independent Events
Outcome of one does not affect the probability of outcome of the other
Experimental Probability
Probability that involves an experiment or game.
