Counting Rules

Question 1

You have a set of n objects that you want to place without replacement

Answer 1

n * (n-1) * (n-2) *…*2*1 = n!

Question 2

You have a set of n objects that you want to place in r spots in a given order.

Answer 2

nPr = n!/ (n-r)!

Question 3

You have a set of n objects from which you want to place r of them in any order.

Answer 3

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

Question 4

Multiplication Rule (or Sausage rule)

Answer 4

imagine you have k “bags” with n1,n2,…,nk objects inside respectively.

Then the number of ways of forming a set by selecting an element from each “bag” is :

n1*n2*…*nk

Question 5

Birthday problem

Answer 5

key: S contains n-vectors such that each entry of the vector represents the possible birthday of a SINGLE person.

Question 6

Fish-in-the-lake

Answer 6

Use: when there is two or more types of objects

Where:

• N = total number of objects
• n = size of the sample
• a = number of tagged objects in total
• x = number of tagged objects in sample