Answer to Question #327149 in Statistics and Probability for Acsiel s velasquez

Question

How many possible samples does it have when a population consist of 12 and you have to get a sample size of 4 from it. *

Answer 1

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

$\begin{pmatrix} N \\ n \end{pmatrix}=\cfrac{N! } {n! \cdot(N-n)! };\\ \begin{pmatrix} 12 \\ 4 \end{pmatrix}=\cfrac{12! } {4! \cdot8! }=\cfrac{9\cdot10\cdot11\cdot12}{2\cdot3\cdot4}=495.$