Answer to Question #300704 in Statistics and Probability for Anna

Question

How many possible samples of size n=8 can be drawn from a population of size 11

Answer 1

$i)$ without replacement

The size of the population is $N=11$. If samples of size $n=8$ are to be selected from this population without replacement then, the number of possible samples is $\binom{N}{n}=\binom{11}{8}=165$.

$ii)$ with replacement

The number of possible samples of size $n=8$ that can be selected from a population of size $N=11$ with replacement is, $N^n=11^8=214358881$