Answer to Question #339803 in Statistics and Probability for roy

Question

Given the population 1,3,4,6 and 8. Suppose samples of size 3 are drawn from this population. How many different samples can be drawn from this population?

Answer 1

Consider the samples without replacement (order of elements in samples does not matter). There are $C_5^3=\frac{5!}{3!2!}=10$ different samples. Consider samples with replacement(order of elements in sample matters). There are $5^3=125$ different samples. We used basic facts from combinatorics to compute a number of samples in both cases.

Answer: there are $10$ different samples without replacement (order of elements in samples does not matter) and $125$ different samples with replacement (order of elements in samples matters).