Question

A restaurant lunch special allows the customer to choose four vegetables from the following group: carrots, cauliflower, peas, radishes, arugula, corn, fiddleheads, onion, broccoli. How many outcomes are possible if the customer chooses four different vegetables?

a) 84
b) 126
c) 210
d) 336

Answer 1

The customer can create 126 different combinations of four vegetables from a selection of nine.

Step-by-step explanation:

The number of possible outcomes when choosing four different vegetables from a set is a problem of combinations. As there are nine vegetable choices and a customer chooses four, we use the combination formula, which is:

C(n, k) = n! / (k!(n-k)!)

For this question, n is 9 (total number of vegetables) and k is 4 (the number of vegetables chosen).

Thus:

C(9, 4) = 9! / (4!(9-4)!) = 9! / (4!5!) = (9×8×7×6) / (4×3×2×1) = 3024 / 24 = 126.

Therefore, the customer has 126 different combinations to choose from.