You have 4 diff. types of vegetables and 7 different types of fruit. 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.

Question

(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

(4 choose 3) * (7 choose 4)

(4 choose 3) = 4

(7 choose 4) = 7*6*5 *4 ! / (3! 4!) = 7*6*5 / 3! <-- 4! cancels

= 7*6*5 / 6

= 35

4 * 35 = 140

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