Answer to Question #257740 in Statistics and Probability for Manu

Question #257740

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 


1
Expert's answer
2021-11-01T11:47:13-0400

Given: n=3,N=9n=3, N=9

Use the formula for combinations

C(n,r)=n!(nr!).r!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)=9!(93!).3!=9!6!.3!=9.8.7.6!6!.3.2=84C(9,3)=\frac{9!}{(9-3!).3!} \\=\frac{9!}{6!.3!} \\=\frac{9.8.7.6!}{6!.3.2} \\=84

Option (b) is correct.


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