Finite MAth
posted by Bryan .
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?

(1) first
Veg
combinations of 6 things taken 3 at a time
= 6!/[3!(63)! ] = 6*5*4/(3*2) = 20
Fruit
= 9!/[ 3! (93)! ] = 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