Answer to Question #339678 in Statistics and Probability for hershey

Question

DETERMINE THE NUMBER OF SETS OF ALL POSSIBLE RANDOM SAMPLES THAT CAN BE DRAWN FROM THE GIVEN POPULATION BY USING THE FORMULA, _NC_n.N = 5, n = 3.

Answer 1

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

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

$_{5}C_3=\cfrac{5! } {3! \cdot(5-3)! }=\cfrac{4\cdot5}{2}=10.$