How many possible samples of size 4 can be made from a population that consists of 6 elements?

The number of possible samples of size 4 from a population of 6 can be calculated using the combination formula. The combination formula is:

C(n, k) = n! / [k!(n-k)!]

where:

• n is the total number of items,
• k is the number of items to choose,
• "!" denotes factorial, which means multiplying all positive integers up to that number.

In this case, n is 6 (the total number of elements) and k is 4 (the size of the sample we want to create).

So,

C(6, 4) = 6! / [4!(6-4)!]

Calculating the factorials:

6! = 654321 = 720 4! = 4321 = 24 (6-4)! = 2! = 2*1 = 2

Substitute these values back into the formula:

C(6, 4) = 720 / (24*2) = 720 / 48 = 15

So, there are 15 possible samples of size 4 that can be made from a population that consists of 6 elements.