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

Answer: She could create 60 platters.

Explanation:

Given: A salad bar offers vegetable platters in 4 sizes (small, medium, large, and super-sized) and 6 different vegetables to choose from.

Number of combinations of selecting r things from n things is given by:-

`^nC_r=(n!)/(r!(n-r)!)`

So, the number of combinations of selecting 2 different vegetables from 6 =
`^6C_2=(6!)/(2!4!)=(6*5)/(2)=15`

Now, By Fundamental counting principle, the number of different platters she could create = (number of ways of selecting 2 different vegetables from 6) x (Number of sizes)

= 15 x 4

= 60

Hence, she could create 60 platters.