FCN
Factorial Notation
Permutations
Permutations with Duplicates
Combinations
100

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.

100

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.

100

What is the formula for calculating permutations?

nPr = n!/(n-r)!
100

How does the presence of identical objects change the formula for counting permutations?

n!/a!*b!*c!
100

What is a combination?

A combination is a selection of items where the order does not matter.

200

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")

200

Simplify and evaluate: 5!

5 x 4 x 3 x 2 x 1 = 120

200

Find the number of ways to arrange 5 people in a row from a group of 10.

10P5 = 30240

200

How many ways can the letters in "SCHOOL" be arranged?

6!/2! = 360

200

How many ways can you choose 2 fruits from a basket of 5 different fruits?

5C2 = 10

300

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.

300

How many different ways can Amy and Tony schedule their 7-day vacation with one activity per day?

7! = 5040

300

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

300

How many ways can Jess walk 9 blocks north and 4 blocks west if she only walks north or west?

13!/9!*4! = 

300

You have 10 books and want to select 3 to read. How many different ways can you choose 3 books?

10C3 = 120

400

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.

400

How many permutations can be made from 24 people standing in line?

24! = 6.204×10^23

400

Sam has 175 songs. How many ways can the first two songs be played without repeating?

175 x 174 = 30450

400

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

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

500

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.

500

Solve for n: (n+3)!/(n+1)! = 56

n = 5

500

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

500

How many ways can you arrange the letters in "MISSISSIPPI"?

34650

500

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

M
e
n
u