Suppose from a population of 50 bank accounts we want to take a random sample of three accounts in order to learn about the population. How many different random samples of three accounts are possible.
To calculate the number of different random samples of three accounts, we can use the combination formula. The formula for combination, also known as "n choose k" or "nCk," is given by:
C(n, k) = n! / (k!(n - k)!)
Where:
n is the total number of items in the population
k is the number of items to be selected in each sample
! denotes the factorial of a number
In this case, we have 50 bank accounts in the population (n = 50), and we want to select 3 accounts in each sample (k = 3).
Using the formula, we can calculate the number of different random samples of three accounts:
C(50, 3) = 50! / (3!(50 - 3)!)
= 50! / (3!47!)
= (50 * 49 * 48) / (3 * 2 * 1)
= 19,600
Therefore, there are 19,600 different random samples of three accounts possible from a population of 50 bank accounts.