FCN
What is the Fundamental Counting Principle (FCP)?
The Fundamental Counting Principle (FCP) states that if one event can occur in m ways and a second event can occur in n ways, then the two events together can occur in m×n ways.
What is factorial notation, and what symbol is used to represent it?
Factorial notation is represented by the symbol "!" and means multiplying a series of descending natural numbers.
What is the formula for calculating permutations?
How does the presence of identical objects change the formula for counting permutations?
What is a combination?
A combination is a selection of items where the order does not matter.
When would the Fundamental Counting Principle not apply?
The FCP does not apply when events are dependent on each other, meaning the outcome of one event affects the outcome of another. (When you see the word "OR")
Simplify and evaluate: 5!
5 x 4 x 3 x 2 x 1 = 120
Find the number of ways to arrange 5 people in a row from a group of 10.
10P5 = 30240
How many ways can the letters in "SCHOOL" be arranged?
6!/2! = 360
How many ways can you choose 2 fruits from a basket of 5 different fruits?
5C2 = 10
Tara can choose between 4 car colors and 3 seat materials. How many combinations are possible?
4×3=12 possible combinations of car colors and seat materials.
How many different ways can Amy and Tony schedule their 7-day vacation with one activity per day?
7! = 5040
A baseball coach has chosen the first two players for the batting order. How many different ways can the rest of the lineup be arranged? (9 Players)
7! = 5040
How many ways can Jess walk 9 blocks north and 4 blocks west if she only walks north or west?
13!/9!*4! =
You have 10 books and want to select 3 to read. How many different ways can you choose 3 books?
10C3 = 120
A postal code consists of 6 total alternating letters and numbers. How many possible postal codes exist with no repetition of characters?
26×10×25×9×24×8=11,232,000.
How many permutations can be made from 24 people standing in line?
24! = 6.204×10^23
Sam has 175 songs. How many ways can the first two songs be played without repeating?
175 x 174 = 30450
A word consists of 10 letters, where 3 are A's and 2 are B's. How many distinct ways can the letters be arranged?
302,400
A teacher is forming a 4-person committee from a group of 8 boys and 7 girls. How many ways can the committee be formed if it must include exactly 2 boys and 2 girls?
8C2 x 7C2 = 588
How many different ways can you select 2 appetizers, 3 main courses, and 1 dessert from a menu of 4 appetizers, 6 main courses, and 3 desserts?
4×3×6×5×3=1,080 ways.
Solve for n: (n+3)!/(n+1)! = 56
n = 5
How many different ways can 5 students be arranged in a line if two of them must stand together?
4! x 2! = (4 x 3 x 2 x 1) x (2 x 1) = 48
How many ways can you arrange the letters in "MISSISSIPPI"?
34650
A deck of cards is dealt into 5-card hands with at most 2 face cards. How many different hands can be dealt?
2,406,768