Counting and functions

Question 1

Ordered choice with repetitions

Answer 1

n^k

Question 2

Ordered choice without repetitions

Answer 2

n!/(n-k)!

Question 3

Unordered choice without repetitions

Answer 3

n!/k!(n-k)!

Question 4

Unordered choice with repetitions

Answer 4

(k+n-1) choose (n-1)

Question 5

What does n stand for

Answer 5

Number of choices

Question 6

What does k stand for

Answer 6

Number of spots to fill / how many we are working with

Question 7

How to calculate n choose k

Answer 7

n! / k!(n-k)!

Question 8

For function f(x) where A -> B. What is the domain?

Answer 8

A is the collection of possible input, its the domain of f

Question 9

For function f(x) where A -> B. What is the codomain?

Answer 9

B is the codomain of f, its the types of outputs f will generate

Question 10

Range

Answer 10

A set of all values that the function actually produces, in most cases in a subset of the codomain

Question 11

We can have:

Answer 11

• Several inputs correspond to the same output
• There is a value in B which never be an output value

Question 12

We cannot have:

Answer 12

• One input corresponds to two different outputs
• There is a value in A which is not an input value

Question 13

Function Composition

Answer 13

Given any two functions f ∶ B → C, g ∶ A → B, we can combine these functions via function composition: that is, we can define the function f ○ g ∶ A → C, defined by the rule f ○ g(x) = f (g(x)). We pronounce the small open circle symbol ○ as “composed with.”