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

    (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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