Question

A population consists of 8 items. The number of different simple random samples of size 3 (without replacement) that can be selected from this population is:

A) 512
B) 56
C) 128
D) 24

Answer 1

The number of different simple random samples of size 3 (without replacement) that can be selected from a population of 8 items is 56.

Step-by-step explanation:

The number of different simple random samples of size 3 (without replacement) that can be selected from a population of 8 items can be calculated using the combination formula. The formula for combinations is n choose r, where n is the total number of items in the population and r is the size of the sample. In this case, we have 8 items and we want to choose 3, so the number of possible samples is 8 choose 3. Using the formula, this can be calculated as:

C(8, 3) = 8! / (3! * (8-3)!) = 56

Therefore, the number of different simple random samples of size 3 that can be selected from this population is 56. So, the answer is B) 56.