Answer to Question #323322 in Statistics and Probability for eli

Question

How many possible samples of size n = 9 can be drawn from a population of size 12?

Answer 1

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

$\begin{pmatrix} N \\ n \end{pmatrix}=\cfrac{N! } {n! \cdot(N-n)! }=\\ =\begin{pmatrix} 12\\ 9 \end{pmatrix}=\cfrac{12! } {9! \cdot3! }=\\ =\cfrac{10\cdot11\cdot12}{2\cdot3}=220 .$