Question

A populations consists of the following five values: 2, 3, 5, 7, 10.

List all possible sample of size 3.

Answer 1

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

$\begin{pmatrix} N \\ n \end{pmatrix}=\cfrac{N! } {n! \cdot(N-n)! }=\\ =\cfrac{5! } {3! \cdot2! }=\cfrac{4\cdot5}{2}=10.$

All the possible samples of sizes n=3 wich can be drawn without replacement from the population:

$\{ (2,3,5), (2,3,7),(2,3,10),(2,5,7),(2,5,10),\\ (2,7,10),(3,5,7),(3,5,10),(3,7,10),(5,7,10)\}.$