A sample of four supermarkets is to be selected from a total of eight in a small town. How many different random samples without replacement can be drawn?
To find the number of different random samples without replacement that can be drawn, we need to use the concept of combinations. In this case, we want to select four supermarkets out of a total of eight.
The formula to calculate the number of combinations is:
C(n, r) = n! / (r! * (n-r)!)
Where:
- n represents the total number of items (in this case, supermarkets)
- r represents the number of items to be selected (in this case, the sample size)
In this case, we have:
- n = 8 (total number of supermarkets)
- r = 4 (number of supermarkets to be selected)
Using the formula, we can calculate the number of combinations:
C(8, 4) = 8! / (4! * (8-4)!)
= 8! / (4! * 4!)
= (8 * 7 * 6 * 5 * 4!) / (4! * 4 * 3 * 2 * 1)
= (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1)
= 70
Therefore, there are 70 different random samples without replacement that can be drawn.
To find the number of different random samples without replacement that can be drawn, we can use the concept of combinations.
The total number of supermarkets in the town is 8, and we want to select a sample of 4 supermarkets from these 8 without replacement.
The number of different random samples without replacement can be calculated using the formula for combinations:
nCr = n! / (r!(n-r)!),
where n is the total number of supermarkets and r is the number of supermarkets to be selected.
In this case, we have n = 8 and r = 4. Substituting these values into the formula, we get:
8C4 = 8! / (4!(8-4)!) = 8! / (4! * 4!) = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70.
Therefore, there are 70 different random samples without replacement that can be drawn from the four selected supermarkets.