Permutations and Combinations

Question 1

Types of selections,

description

permutations

combinations

Answer 1

Finding the number of distinct arrangements or selections from a given number of objects

Permutation if the order of the object is important

Combination if the order of the object is not important

Question 2

Factorials,

description

formula/rule

Answer 2

The factorial of a number n is the product of all the natural numbers up to and including n

n! = n x (n - 1) x (n - 2) x … x … 2 x 1 where n is a natural number

Question 3

Arrangements,

different objects in a line

objects in a line if there are more than one similar type

objects in a circle or ring

Answer 3

The number of ways of arranging n unlike objects in a line is: n!

The number of ways of arranging n objects in a line if p of them are of one type (repeats) is:
n! / (p! x q!)
p being the amount of repeats of the element
q being the total number of elements that have repeats

The number of ways of arranging n unlike objects in a ring is: (n - 1)!

Question 4

Permutations formula

Answer 4

To work out the number of permutations of r elements from a set of n elements:
nPr = n! / (n - r)!

Question 5

Combinations formula

Answer 5

To work out the number of combinations of r elements from a set of n elements:
nCr = n! / [ (n - r)! r! ]