. Assume that you have 6 different types of vegetables and 6 different types of fruit.

Question

A vegetable salad consists of a mixture of any 3 types of vegetables, and a fruit salad consists of a mixture of 4 kinds of fruit.

(1) In how many different ways can you prepare a vegetable salad and a fruit salad?

(2) In how many different ways can you prepare a vegetable salad or a fruit salad but not both?

(3) How many ways can you choose two different kinds of salad?

Answer 1

Recommend using an nCr calculator or the equation C = (n!) / (r!( n! - r!)), where n is the total number of options and r is the number of selections.

1) For Vegetable Salads, n = 6 and r = 3. 20 Vegetable Salad combinations.

For Fruit Salads, n = 6 and r = 4. 15 Fruit Salad Combinations.

2) You add the two combinations together since you choose one salad type or the other. 20 + 15 = 35.

3) This one is unclear if you can have any two types of salads or if it is one of each. I am assuming it can be any two salads and does not need to be one of each. In this case, n = 35 and r = 2. You get 595 possible combination.

If it is one of each type, you multiply the two combinations together since you first select 1 from the 20 veggie salads and then 1 from the 15 fruit salads. 20 x 15 = 300.