Answer:
21 combinations.
Explanation:
AI-generated answer
If you sample with replacement, each time you draw a name from the hat, you put it back before drawing again. This means that the same name can be selected more than once in each draw.
To calculate the number of combinations when sampling with replacement, you raise the number of options (7 names) to the power of the number of draws (2).
So, in this case, when sampling with replacement, you can have 7^2 = 49 combinations.
If you sample without replacement, each time you draw a name from the hat, you do not put it back. This means that once a name is selected, it is removed from the available options for subsequent draws.
To calculate the number of combinations when sampling without replacement, you use the formula for combinations. The formula for combinations is nCr = n! / (r!(n-r)!), where n is the number of options and r is the number of draws.
In this case, you have 7 options and want to draw 2 names. So, the number of combinations when sampling without replacement is 7! / (2!(7-2)!) = 7! / (2!5!) = (7 * 6) / (2 * 1) = 21.