Question

Consider a population consisting of 4, 7, 8, 13, 15 and 17. Suppose samples of size 3 are drawn from this population. Determine the total number of samples. *

Answer 1

The number of possible samples which can be selected without replacement is

$\begin{pmatrix} N \\ n \end{pmatrix}=\cfrac{N! } {n! \cdot(N-n)! }=\\ =\begin{pmatrix} 6\\ 3 \end{pmatrix}=\cfrac{6! } {3! \cdot3! }=\cfrac{4\cdot5\cdot6}{2\cdot3}=20 .$