Combinatorics

Question 1

Total outcomes of n1 to nk

Answer 1

= n1 x n2 x … x nk

Question 2

Sum Rule

Answer 2

A and B for n … nk amount of outputs = A applied to n … nk + B applied to n … nk

Question 3

Disjoint

Answer 3

Independent

Question 4

Permutations

Answer 4

An ordering of an elements in a set. Normally found using the factorial of the amount.
S = {1,2,3}
Permutations:
1,2,3
3,2,1
2,3,1
etc.
Has s! amount of combinations/permutations.

Question 5

n!

Answer 5

N factorial, has a specific way of representing it using pi notation.

Question 6

K-Permutations

Answer 6

n! / (n-k)!
Order matters.

Question 7

K-Combinations / Binomial coefficient

Answer 7

C(n,k) = n! / (n-k)! * k!
No order.
Can also be represented as:
(n)
(k)

Question 8

Order and No Order Explanation.

Answer 8

Order Matters means that if there is a representation of k that k contains both {5,4} and {4,5}, it needs to be shown. No Order means that if there is {4,5}, we don’t care that there is a {5,4} as it counts as a duplicate, therefore we also divide by k!.

Question 9

Product Rule

Answer 9

n1 …. nk = n1 x n2 x … x nk

Question 10

Sum Rule

Answer 10

If A and B are disjoint events and there are n1 possible outcomes for event A
and n2 possible outcomes for event B then there are n1 +n2 possible outcomes
for the event “either A or B”.

Question 11

Disjoint Events

Answer 11

Two events are said to be disjoint (or “mutually exclusive”) if they can’t occur
simultaneously.
Example: If you have 3 pairs of blue jeans and 2 pairs of black jeans, then there
are 3 + 2 =5 different pairs of jeans which are blue or black which you could
wear.