Combinatorics

Question 1

Multiplication principle of combinatorics

Answer 1

The amount of combinations of items from different sets, assuming one item per set, is equal to the product of the number of items on each set.

Example, pairs of trousers and shoe combinations = n trousers * p shoes

Question 2

What is permutation and what is combination?

Answer 2

A permutation is an arrangement of things in different orders, whereas combination is simply concerned with combining things.

Permutation = Order matters
Combination = Order does not matter

Question 3

Order matters, no repetition

Answer 3

nPr = n!/(n-r)!

Where n = total number of items on the set to choose from and r = number of items in the permutation

Question 4

Order doesn’t matter, no repetition

Answer 4

nCr = n!/r!(n-r)!

Where n = total number of items on the set to choose from and r = number of items in the combination

Question 5

Order matters, repetition allowed

Answer 5

nPr = n^(r)

Question 6

Order doesn’t matter, repetition allowed

Answer 6

nCr = (n+r - 1)!/r!(n-1!)