10 Mathematics: Quarter 3

Quarterly Exam Reviewer - Permutation and Combination - Mutually Exclussive

Cardinality

It is the number of elements in a given set.

Tree Diagram

A device used to list all possibilities of a sequence of events in a systematic way.

n1 x n2 x n3 x … ways

The fundamental counting principle states that if one event can occur in n1 ways, a second event can occur in n2 ways, and a third event can occur in n3 ways, and so on, then these events can occur in ______________

Permutation

The arrangement of objects in which order is important

n!

If n is equal to r, then nPr=___

1

If r is equal to 0, then nPr=___

n

If r is equal to 1, then nPr=___

nPr = n! / (n - r)!

The formula for permutation

Distinguishable Permutation

The arrangement of objects with identical objects.

P = n! divided by n1!n2!n3!…nk!

Formula for distiguishable objects

Circular Permutation

The arrangement of objects in a circular manner

P= n!/n or P= (n - 1)!

Formula for circular permutation

P= (n - 1)! divided by 2

Formula for circular permutation (key ring)

P= [(n - 1) - 1]! 2!

Formula for circular permutation if 2 wanted to be together

(n - 1)!
minus
[(n - 1) - 1]! 2!

Formula for circular permutation if 2 does not want to be together

Combination

An arrangement of n objects with no repetitions and the order is NOT important

nCr= nPr divided by r!

or

nCr= n! divided by (n - r)! r!

Formula for combination

Mutually Exclusive Events

This is when the events are impossible to happen at the same time

P(A U B)= P(A) +P(B)

Mutually Exclusive Events Formula

Non-Mutually Exclusive Events

This is when the events are can happen at the same time

P(A U B)= P(A) +P(B) - P(A ∩ B)

Non-Mutually Exclusive Events Formula

Dependent Events

The result of one event can affect the result on another event

Independent

The result of one event does NOT affect the result on another event

P(A and B)= P(A) x P(B)

Independent Formula

P(A and B)= P(A) x P(B/A)

Dependent Formula

Sample Space

The set of elements

1

In a dependent event P(A and B)= P(A) x P(B after A is taken)

The sample events in P(B/A) will be reduced by ___