In designing an experiment involving a treatments applied to 5 test subjects, researchers plan to use a simple random sample of 5 subjects from 28.

How many different simple random samples are possible?

To calculate the number of different simple random samples possible, we can use the combination formula.

The number of different simple random samples is given by the combination formula:

nCr = n! / r!(n-r)!

In this case, we have a total of 28 test subjects (n = 28) and we want to choose 5 subjects (r = 5) for each sample. Plugging these values into the combination formula, we get:

28C5 = 28! / 5!(28-5)!
= 28! / 5!23!

Simplifying further:

28C5 = (28 * 27 * 26 * 25 * 24) / (5 * 4 * 3 * 2 * 1)

Calculating this expression gives us:

28C5 = 98,280

Therefore, there are 98,280 different simple random samples possible.

To determine the number of different simple random samples, we need to calculate the number of ways we can select 5 subjects from a group of 28.

This can be calculated using the combination formula, also known as the binomial coefficient, which is given by:

C(n, k) = n! / (k! * (n - k)!)

Here, n represents the total number of subjects in the group, and k represents the number of subjects we want to select.

In this case, n = 28 and k = 5. Plugging these values into the formula:

C(28, 5) = 28! / (5! * (28 - 5)!)

Simplifying this calculation:

C(28, 5) = (28 * 27 * 26 * 25 * 24) / (5 * 4 * 3 * 2 * 1)

Therefore, the number of different simple random samples possible is:

C(28, 5) = 98,280