Answer to Question #339680 in Statistics and Probability for micaely

Question

DETERMINE THE NUMBER OF SETS OF ALL POSSIBLE RANDOM SAMPLES THAT CAN BE DRAWN FROM THE GIVEN POPULATION BY USING THE FORMULA, NCn.

N = 10, n = 3

Answer 1

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

$_NC_n=\cfrac{N! } {n! \cdot(N-n)! };$

$_{10}C_3=\cfrac{10! } {3! \cdot(10-3)! }=\cfrac{8\cdot9\cdot10}{2\cdot3}=120.$