# Finite MAth

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Assume that you have 6 different types of vegetables and 9 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 3 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?

• Finite MAth -

(1) first
Veg
combinations of 6 things taken 3 at a time
= 6!/[3!(6-3)! ] = 6*5*4/(3*2) = 20

Fruit
= 9!/[ 3! (9-3)! ] = 9*8*7*6*5*4/(6*5*4*3*2)
= 9*8*7/6
= 12*7 = 84

(2) 20+84 = 104

for veg 1, 84 different fruits
for veg 2, 84 different fruits
etc
so 20* 84 = 1680

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