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**Order does matter 1234≠4321**Order does matter 1234≠4321Counting Techniques

Permutation:

The number of ways of arranging a set of objects

e.g. A B C De.g. A B C D

Total =4x3x2x1 =24 =4!Total =4x3x2x1 =24 =4!

P=Permutationr=placesP=Permutationr=places

e.g. Any 4 letter permutation 26 25 24 23 26!26-4! =26!22! 26x25x24x23x22x21x20x19… 22x21x20x19x18x17x16x15…ce.g. Any 4 letter permutation 26 25 24 23 26!26-4! =26!22! 26x25x24x23x22x21x20x19… 22x21x20x19x18x17x16x15…c

P= Does not allow repetition P= Does not allow repetition e.g. Bike Lock (allows to repeat number) 10P4 = 10!6! X Does not work 10 10 10 10 104= 10,000e.g. Bike Lock (allows to repeat number) 10P4 = 10!6! X Does not work 10 10 10 10 104= 10,000

Permutations of Objects, not all Different:

e.g.

Addition Principle:

e.g.

U= union ∩= IntersectionU= union ∩= Intersection

Inclusion- Exclusion Principle:

Is when we include the numbers of the first set, exclude the numbers of the two set intersection, then include the numbers of the 3 set intersection

https://www.youtube.com/watch?v=szUTQRJU76Q&index=27&list=FLmBm2NbG4Ovc8ep4wASKaFg&t=0s

-use this for when there are sets that are non-mutually and interlay

- we can either use the easier way, of drawing a ven diagram or we could also use the formula

|A|, | | means the elements of A|A|, | | means the elements of A

Don’t forget to subtract the 2 intersects from A∩B∩C

And there also might be some that are neither A, B or C

But there are also formulas

e.g.

Arrangements of Objects with Some Restrictions Imposed:

This is for when there are certain restrictions where certain things (e.g. numbers or letter) can be.

The best way of thinking about is that there are n-1 options and n-1 places if a object has to go in a specific place

And if two objects have to be together then u count them as just one, but also remember that there are n numbers of places that they could be.

e.g.

e.g.

e.g.

Additive and Multiplicative Reasoning:

You add how many times A can happen but not B and B can happen and not A and How many both can happen

e.g.

e.g.

Combinations:

e.g.

** One With Subsets