To find the number of combinations of three scoops of ice cream that Laura can choose from, we need to consider whether repetition is allowed.
1. If repetition is allowed:
In this case, Laura can choose the same flavor for more than one scoop. Since she has 6 flavors to choose from and repetition is allowed, she can choose any flavor for each of the three scoops.
The number of possible combinations can be calculated using the formula:
Number of combinations = (number of options)^(number of choices)
In this case, since Laura has 6 options (flavors) and she needs to choose 3 scoops, we can calculate the number of combinations as follows:
Number of combinations = 6^3 = 216
Therefore, there are 216 possible combinations of 3 scoops of ice cream that Laura can choose from when repetition is allowed.
2. If repetition is not allowed:
In this case, Laura can choose each flavor only once for the three scoops.
The number of possible combinations can be calculated using the formula for combinations:
Number of combinations = n! / (r! * (n-r)!)
Where n is the total number of options (flavors) and r is the number of choices (scoops).
In this case, n = 6 (flavors) and r = 3 (scoops).
Substituting the values:
Number of combinations = 6! / (3! * (6-3)!)
= 6! / (3! * 3!)
= (6 * 5 * 4 * 3 * 2 * 1) / ((3 * 2 * 1) * (3 * 2 * 1))
Simplifying the expression:
Number of combinations = (6 * 5 * 4) / (3 * 2 * 1)
= 20
Therefore, there are 20 possible combinations of 3 scoops of ice cream that Laura can choose from when repetition is not allowed.
In summary, if repetition is allowed, there are 216 possible combinations, and if repetition is not allowed, there are 20 possible combinations of 3 scoops of ice cream that Laura can choose from.