Permutation and Combination

Permutation and Combination

Factorial:

n! = n*(n-1)*(n-2)*...*1
0! = 1

Permutation:

nPr = n! / (n-r)!

Combination:

nCr = n! / [r!(n-r)!]
nCr = nC(n-r)
nCr + nC(r-1) = (n+1)Cr

When to use:

Wording	Use
Arrange, order, rank, seat	Permutation
Select, choose, committee, team	Combination
At least one	Total - none
Identical objects	Divide by repeated factorials

Arrangements:

n distinct in a row = n!
n distinct in a circle = (n-1)!
If clockwise and anticlockwise same, circular arrangements = (n-1)!/2

Repeated letters:

Arrangements of n letters with repeats a,b,c:
n! / (a!b!c!)

Gap method:

• Use for "no two together".
• Arrange non-restricted objects first.
• Place restricted objects in gaps.

Block method:

• Use for "must be together".
• Treat grouped objects as one block.
• Multiply by internal arrangements.