Question

A finite population consists of four elements: 6, 1, 5, 3. (a) how many different samples of size n = 2 can be selected from this population if you sample without replacement? (sampling is said to be without replacement if an element cannot be selected twice for the same sample.)

Answer 1

Since the order of elements doesn't matter, we use the formula for combination as follows.

$nCk= \frac{n!}{k!(n-k)!}$

So the number of ways to choose 2 elements from a set of 4 elements would be
$4C2= \frac{4!}{2!(4-2)!}=6$

Thus the answer is 6.