Determine the size of the sample space

Question

An experiment consists of choosing a subset from a fixed number of objects where the arrangement of the chosen objects is not important. Determine the size of the sample space when you choose the following:

 

1) 2 objects from 15= 

2) 4 objects from 6=

3) 8 objects from 18=

 

 

 

 

Answer 1

Dalia,

 

Since arrangement does not matter (i.e. A, B, C is the same as C, B, A) you have a combination problem, as the total sample space is the total number of possible combinations. In this case you have sample spaces of

15, C, 2

6, C, 4

and

18, C, 8

 

The formula for combination given n, C, r is

n!/[(r!)(n-r!)] (sometimes k is used instead of r)

 

So for 15, C, 2, you have 105 items in the sample space as

 

15!

--------  = 15 x 14 / 2 = 15x7 = 105

2!(13!)

 

Repeat for the other two.