Fundamental Counting Principle
What operation do I use to solve problems using the Fundamental Counting Principle?
Multiplication
What is 7!
5040
True or False
Order matters when solving a combination counting problem
False
How many ways can you choose 2 marbles from a bag of 7 different marbles if you do not put the first marble back?
42
You are going back-to-school shopping. You can choose from 3 binders, 4 highlighters, and 3 pens. How many ways can you get one of each?
36
How many ways can you arrange 5 people in a row?
120
Is the following a Permutation or a Combination?
How many 4-digit codes can be made using the digits 1-7, no repetition
840
3 people are chosen at random from a group of 5 men and 10 women. What is the probability that all 3 are men? (Round to 5 decimal places)
0.02198
A deli offers 6 sandwiches, 6 drinks, and 4 desserts. How many different combinations can you make if you choose one from each category?
144
(8!)/(5!)
336
Is the following a Permutation or a Combination?
In how many ways can we select a President, Vice President, Secretary, and Treasurer from a group of 40 students?
Permutation
A shepherd is asked to choose his 3 favourite sheep to compete in a sheep beauty pageant. How many ways can he choose them from his flock of 10?
120 ways
A card is drawn at random from a standard 52-card deck. Find the probability that the card is a king given that it is a face card. (Leave as a fraction)
1/3
You have 6 ways to go from your house to downtown and 4 ways to go from downtown to work. How many ways can you go from your house to work if you must stop downtown?
24
(8!)/(2!3!)
3360
Is the following a Permutation or a Combination?
In how many ways can we deal 3 face cards in a standard deck of cards?
Combination (The order in which you receive the cards doesn't matter for most card games)
A password is 3 letters followed by 3 digits. How many possible passwords have the order consonant, vowel, consonant, even, odd, even? Repetition is possible.
21x5x21x5x5x5 = 275 625
An archer has probability 0.6 of hitting the target. Find the probability that she hits the target exactly 3 times in 5 attempts. (Round to 4 decimal places)
0.3456
If you cannot repeat letters or numbers, how many license plates can you make from 3 letters and 4 numbers?
78,624,000 License Plates
(12!) / ((12-3)!3!)
220
Is the following a Permutation or a Combination?
In how many ways can you order the letters in the word BUBBLE?
Permutation
How many ways can you make a starting basketball line-up of 5 players from a team of 12 players?
792