A drink order at Sonique consists of exactly one soft drink combined with zero o

Question

A drink order at Sonique consists of exactly one soft drink combined with zero or more real fruit garnishes and zero or more flavor mixins. Six soft drinks are on the menu: Root Beer, Cola, Electrolyte Booster, Lemon-Lime, Diet Cola, and Fizzy Orange. Three real fruit garnishes are available: strawberries, cherries, and grapes. There are five flavor mixins to choose from: vanilla, lime, lemon, watermelon, and pineapple.

(a) How many drink orders are possible?

(b) How many drink orders must be placed in order to guarantee that two of them are identical?

Explanation / Answer

a)

There are 6 soft drinks.

There are 4 options for real fruit (including none).

There are 6 options for flavor mixins (including none).

Hence, a total of 6*4*6 = 144 orders [ANSWER]

*********************************

a)

Hence, as n = 144 orders are possible, then we must order

n + 1 = 145 [ANSWER]

to guarantee that two of them are identical.   

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