2.6 Combinatorics and Probability

Question 1

What is the cardinality of a set and how is it written

Answer 1

Number of elements inside |S|

Question 2

What is the cartesian product of two sets A and B (A X B)

Answer 2

The set of ordered pairs

Question 3

What is the cardinality of A X B

Answer 3

|A X B| = |A| X |B|

Question 4

A = {1,2}
B = {a,b,c,d}

what is A X B =
and its cardinality

Answer 4

{(1,a), (1,b), (1,c), (2,a), (2,b), (2,c)}

|A X B| = 2 * 3 = 6

Question 5

If A is a set, the set of ordered n-tuples over A, what is the cardinality

Answer 5

|A^n| = |A|^n

Question 6

A combination lock has 3 digits, each of which is a number from 0-9, how many digits are there?

Answer 6

1000

Question 7

Suppose we want to pick an ordered collection of k elements (without any repeats) from a set of n elements. What is the formula for how many ways we can pick them

Answer 7

(n!) / (n - k)!

Question 8

Pick three winners (ordered) from 8 contestants, how many ways of doing this are there? P(8,3)

Answer 8

8!/5! = 336 ways

Question 9

If we want to pick an unordered collection of k elememts from a set of n elements, what is the formula for how many ways we can pick them?

Answer 9

(n!) / k! (n - k)!

Question 10

What is a partiton

Answer 10

A collection of disjoint events that add up to 1