Giuseppe's fruit stand (just north of Key West in Florida) is famous for their $7 “bag-o-fruit." Each bag contains limes, oranges, grapefruits and kiwis. There are alwaysa total of twenty pieces of fruit in each bag, but depending on what is available, thespecific contents vary.How many different "bag-o-fruit"s are there?

Answered: Giuseppe's fruit stand (just north of…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

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Giuseppe's fruit stand (just north of Key West in Florida) is famous for their $7 “bag-
o-fruit." Each bag contains limes, oranges, grapefruits and kiwis. There are always
a total of twenty pieces of fruit in each bag, but depending on what is available, the
specific contents vary.
How many different "bag-o-fruit"s are there?

Expert Solution

Step 1

Given,

Total number of fruits in the bag = 20

The fruits are limes, oranges, grapes and kiwis.

We have to find the number of different "bag-o-fruit" are there.

Step 2

Let's assume,

number of limes in the bag $= x$

number of oranges in the bag $= y$

number of grapes in the bag $= z$

number of kiwis in the bag $= w$

So,

Total number of fruits $= 20$

$x + y + z + w = 20$

Number of different fruits bags = number of non negative integral solutions of the equation $x + y + z + w = 20$

(When we have the equation $x_{1} + x_{2} + . . . . . . . . + x_{r} = n$ ; then the number of non negative integral solutions of the equation = ${}^{n + r - 1}C_{n}$ )

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