FCP, Permutations,& Combinations
Let's Count
(FCP, P, & C)
(FCP, P, & C)
What are the odds?
Probability
Probably
Probability
Probability
100
Evaluate 6!
6 x 5 x 4 x 3 x 2 x 1 = 720
100
Evaluate 7 C 4
35
100
What is the probability of rolling a number greater than 4 on a fair die?
1/3
100
The table below shows the number of gold, silver, and bronze medals won by the US and China during the 2012 Summer Olympics.
P(US bronze or silver)
57/191
100
A jar has 12 marbles. Four are blue, five are red and the rest are yellow.
Find P(red or yellow)
2/3
200
On Jack’s science quiz there were three multiple choice questions with four choices each and four true/false. How many ways can he answer the questions? Is this a permutation, combination, or fundamental counting principle?
FCP
4 x 4 x 4 = 64 ways
200
A six-sided dice is rolled, a card is drawn from a standard deck of cards, a day of the week is selected, and a month is picked. How many different results are there? Is this a permutation, combination, or fundamental counting principle?
26,208. Fundamental Counting Principle.
200
The table below shows the number of gold, silver, and bronze medals won by the US and China during the 2012 Summer Olympics.
What is the probability of choosing a gold medal for the US?
46/191
200
Erik is randomly choosing a card from a standard deck and flipping a coin. What is the probability that he chooses a card that is red and flips a tail?
1/4
200
A jar has 12 marbles. Four are blue, five are red and the rest are yellow.
Find P(Blue, Blue) with replacement
1/3 x 1/3 = 1/9
300
Marlena must answer 3 out 8 essay questions on her writing quiz. How many ways can she choose three? Is this a permutation, combination, or fundamental counting principle?
56. Combination.
300
Josh must submit 4 paintings as a part of his application to art school. If he has 25 to choose from, how many ways can he pick 4? Is this a permutation, combination, or fundamental counting principle?
12,650. Combination.
300
A group of cell phone owners were asked whether they had an Android or Apple phone. There were 40 android users and 50 iphone users.
Without replacement, what is the probability of choosing an android user and then an iphone user?
4/9 x 5/9 = 20/81
300
A coin is flipped three times. What is the probability that tails comes out each time?
1/8
300
A jar has 12 marbles. Four are blue, five are red and the rest are yellow.
Find P(Blue, Blue) without replacement
1/3 x 3/11 = 1/11
400
The Grandview High School Band plans to play 6 pieces of music in their upcoming concert. How many ways can they arrange the order of their performance? Is this a permutation, combination, or fundamental counting principle?
720. Permutation.
400
The field hockey coach choose players to put away equipment after each practice. If there are 16 players on the team, how many ways can she choose 5? Is this a permutation, combination, or fundamental counting principle?
4,368. Combination.
400
A team’s jerseys are numbered 1-100. Your lucky number is 13. What is the probability of you getting a jersey that is NOT a multiple of 13?
93/100
400
A board game has a challenge round where the player can earn bonus money by rolling a die.
In order to win, a player must roll the die three times. On the first roll, the number must be less than four. On the second roll, the number must be less than three. On the last roll, the number must be less than two. What is the probability of this happening?
1/2 x 1/3 x 1/6 = 1/36
400
A jar has 12 marbles. Four are blue, five are red and the rest are yellow.
Find P(3 yellow) without replacement
1/4 x 2/11 x 1/10 = 1/220
500
How many ways can a president, vice president, and treasurer be elected from a group of 40 students? Is this a permutation, combination, or fundamental counting principle?
59,280. Permutation.
500
How many different 8-letter arrangements can be made using the letters in the word friendly? Is this a permutation, combination, or fundamental counting principle?
Permutation
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
500
Of the 33 sophomores, 15 are taking Algebra 2 and the rest are taking Precalculus. If a sophomore is chosen at random, find the probability of choosing a student who takes Algebra 2 and then a student who is taking Precalculus. Students are chosen and not replaced.
5/11 x 9/16 = 45/176
500
There are 18 pens in a drawer. Half of them are red. The number of blue in the drawer is two less than the number of red, and the rest are black.
Without replacement, what is the probability of choosing 3 black pens in a row?
0