How many different simple random sample of size 8 can be obtained from a population whose size os 42?
To find the number of different simple random samples of size 8 that can be obtained from a population of size 42, we can use the formula for combinations, also known as binomial coefficients.
The formula for calculating combinations is given by:
C(n, r) = n! / (r! * (n - r)!)
Where:
n is the size of the population
r is the size of the sample
In this case, the population size is 42 (n = 42) and the sample size is 8 (r = 8). Plugging these values into the formula, we have:
C(42, 8) = 42! / (8! * (42 - 8)!)
Calculating the factorial values:
42! = 42 * 41 * 40 * ... * 3 * 2 * 1
8! = 8 * 7 * 6 * ... * 3 * 2 * 1
34! = 34 * 33 * 32 * ... * 3 * 2 * 1
Simplifying the equation:
C(42, 8) = (42 * 41 * 40 * ... * 3 * 2 * 1) / ((8 * 7 * 6 * ... * 3 * 2 * 1) * (34 * 33 * 32 * ... * 3 * 2 * 1))
After canceling out common factors, we get:
C(42, 8) = (42 * 41 * 40 * ... * 35) / (8 * 7 * 6 * ... * 1)
Now we can calculate the value using a calculator or programming language that supports large numbers. The result is:
C(42, 8) ≈ 188,680 different simple random samples of size 8 can be obtained from a population of size 42.