Question

How many different samples of size n=3 can be obtained from a finite population of size N=9 . 

Select one: a. 42 b. 84 c. 21 d.7 

Answer 1

Given: $n=3, N=9$

Use the formula for combinations

$C (n, r) = \frac{n!}{(n-r!).r!}$

Substitute the given in each letter, where in this question, given population N is for n in the formula, and the given sample size n is for r in the formula.

$C(9,3)=\frac{9!}{(9-3!).3!} \\=\frac{9!}{6!.3!} \\=\frac{9.8.7.6!}{6!.3.2} \\=84$

Option (b) is correct.