Factorial Notations-Into Perms&Coms

Permutation- an ordering of objects in which order matters.
Combination- an ordering of objects in which order doesn't matter.
*The exclamation mark is "factorial"*

Perm VS. Com
We did examples to show the differences between Perms and Coms:

1- How many 5 letter "words", using the alphabet, no repeats?
26*25*24*23*22=7893600
26!=(26*25*24*23*22)*21!
SO 26*25*24*23*22=26!
21!
Divide it by 21(the 6th number) because there are only 5 spaces for the letters to go into.
You can do this on the calculator with this equation:
nPr= n!
(n-r)!
SO 26P5= 26!
(26-5)!
=7893600
Part 1 is a permutation because the order of the letters matters since there are no repeats.

2-How many poker hands are there with hearts/diamonds only?
There are 26 hearts/diamonds alltogether in a 52 card deck, so we go like this:
26*25*24*23*22 = 7893600 = 65780 unique poker hands using hearts/diamonds only.
5 * 4 * 3 * 2 * 1 120
You can do this on the calculator with this equation:
nCr= n!
(n-r)!*r!
SO 26C5= 26!
(26-5)!*5!
The extra *5! is to divide out all combinations with the same 5 elements(the same 5 cards, but in different orders)
Part 2 is a combination because the order doesnt matter.