Combinatorics

nCr : "from n choose r"

n = length of possibility set (ex. 5 letters)
r = length of combination set (ex. pick 2)



Permutation with Repetition
Order matters and elements of the possibility set can be repeated.

nr

	a	b	c	d	e
a	aa	ab	ac	ad	ae
b	ba	bb	bc	bd	be
c	ca	cb	cc	cd	ce
d	da	db	dc	dd	de
e	ea	eb	ec	ed	ee

Permutation without Repetition
Order still matters, but elements cannot be repeated.

n!
(n-r)!

	a	b	c	d	e
a		ab	ac	ad	ae
b	ba		bc	bd	be
c	ca	cb		cd	ce
d	da	db	dc		de
e	ea	eb	ec	ed

Combination without Repetition
Order does not matter, and elements cannot be repeated.

n!
r!(n-r)!

	a	b	c	d	e
a		ab	ac	ad	ae
b			bc	bd	be
c				cd	ce
d					de
e

Combination with Repetition
Order does not matter, but elements can be repeated.

(n+r-1)!
r!(n-1)!

	a	b	c	d	e
a	aa	ab	ac	ad	ae
b		bb	bc	bd	be
c			cc	cd	ce
d				dd	de
e					ee