Answer:
Number of different simple random samples of size 5 that can be selected from a population of size 8 = 56 ways
Explanation:
Step 1: Stating the combination formula
The number of selections of a number n, taking r at a time is given by the formula:
![(n!)/((n - r!)r!)](https://img.qammunity.org/2021/formulas/mathematics/college/iyi19g7p3s8cgjpkgxlx4z6t4x4in31fru.png)
From the formula above, n is population size = 8
r is sample size = 5
Step 2: Substituting the values of n and r
Number of possible selections = 8!/(8 -5)*5! = 8!/3! * 5!
Number of possible selections =
![(8*7*6*5*4*3*2*1)/(3*2*1 * 5*4*3*2*1)](https://img.qammunity.org/2021/formulas/mathematics/college/qwzu5wgc4ku78npd35jorhjt4gqhnhyx3w.png)
Number of possible selections = 56
Therefore, number of different simple random samples of size 5 that can be selected from a population of size 8 = 56 ways