Answer to Question #328311 in Statistics and Probability for Tenshi

Question

A population consists of the numbers 1, 2, 3, 4, 5, 6, 7 and 8. If a sample size is 4. how many possible random samples can be drawn from the given population?

Answer 1

Let n = 8 - population size, k = 4 - sample size.

Amount of different samples is calculated by the formula $C_n^k=\frac{n!}{k!(n-k)!}=\frac{n(n-1)...(n-k+1)}{k!}=\frac{8\cdot7\cdot6\cdot5}{1\cdot2\cdot3\cdot4}=70$