Posted by **Bryan** on Thursday, January 26, 2012 at 9:04pm.

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 -
**Damon**, Thursday, January 26, 2012 at 9:24pm
(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

(3) 20 kinds of veg salad and 84 of fruit salad

for veg 1, 84 different fruits

for veg 2, 84 different fruits

etc

so 20* 84 = 1680

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