Question

A menu lists five vegetable; applesauce, beans, carrots, peas, and potatoes. you decide to order a "vegetable plate" of three (different) vegetables. (one possible choice, for example, is to order beans, carrots and potatoes.) how many choices are available to you

Answer 1

A menu lists five vegetable; applesauce, beans, carrots, peas, and potatoes. A person wants to order a vegetable plate with a combination of any 3 different vegetables from the menu. The total number of choices that the person has can be found using combinatorics, a branch of mathematics dealing with combinations and permutations.

Given: n (items in menu) = 5, r (combination of 3 vegetables) = 3

Substituting the value for n and r in the expression for calculating the available choices,
`^(n)C_(r) = (n!)/((n-r)!r!)`,

We get,

`^(5)C_(3) = (5!)/((5-3)!*3!) = (5*4*3!)/(2!*3!) = (5*4)/(2) = 10`

Therefore, the answer is 10 choices or unique combinations.