Final answer:
To calculate the number of ways to choose 6 ice cream cones from 11 flavors allowing repeats, use the combinations with repetition formula given by C(n + r - 1, r) which equals C(16, 6) in this case.
Step-by-step explanation:
The student is asking about a problem related to combinations and permutations in mathematics, specifically a problem of combinations with repetition (also known as stars and bars). The question involves finding the number of ways to choose 6 ice cream cones from 11 different flavors, where repeats of flavors are allowed.
To solve this, we must use the formula for combinations with repetition: C(n + r - 1, r), where n is the number of items to choose from (flavors), and r is the number of items being chosen (cones). In this case, we have n = 11 and r = 6, so the calculation becomes C(11+6-1, 6) = C(16, 6).
To calculate C(16, 6), we can use the formula for combinations: C(n, r) = n! / (r!(n-r)!), which would result in the number of ways to choose the ice cream cones.