Question

A salad bar offers vegetable platters in 4 sizes (small, medium, large, and super-sized) and 6 different vegetables to choose from. Different platters can be created by changing the size and/or the choice of vegetables. If Selena wants to order a platter with exactly 2 different vegetables, how many different platters could she create?

Answer 1

To calculate the total number of different vegetable platters Selena could create, we find the number of combinations of 2 vegetables from 6 (15 combinations), and multiply by the number of sizes (4), resulting in 60 different platters.

Step-by-step explanation:

The student's question involves figuring out how many different vegetable platters Selena could create, given that she wants to order a platter with exactly 2 different vegetables, there are 4 sizes of platters, and 6 different vegetables to choose from. To solve this problem, we first need to determine the number of ways in which Selena can choose 2 vegetables out of 6. This is a combination problem because the order in which the vegetables are chosen does not matter.

To calculate the number of combinations of 6 vegetables taken 2 at a time, we use the combination formula:

C(n, k) = n! / [k! * (n - k)!]

Substituting 6 for n and 2 for k yields:

C(6, 2) = 6! / [2! * (6 - 2)!] = (6*5) / (2*1) = 15

Now, since there are 4 different platter sizes, each vegetable combination can be assigned to any one of these sizes. Multiplying the 15 vegetable combinations by the 4 sizes gives us the total number of possible platters.

15 vegetable combinations * 4 platter sizes = 60 different platters