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Maria has three identical apples and three identical oranges. How many ways are there for her to distribute the fruits among her four friends if she doesn't give Jacky any oranges? (Note: Maria takes none of the fruit herself, and some of her friends might not receive any fruit at all.)

 
 Oct 8, 2021
 #1
avatar+114812 
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Maria has three identical apples and three identical oranges. How many ways are there for her to distribute the fruits among her four friends if she doesn't give Jacky any oranges? (Note: Maria takes none of the fruit herself, and some of her friends might not receive any fruit at all.)

 

I have used what is called the 'Stars and Bars' method.

 

I get 200 ways

 

put the 3 apples in a row, they are the stars.  Use bars to divide them into 4 piles, you will need 3 bars

So you have 3 apples and 3 bars so there are  6C3 places to put the bars = 20 possible ways to distribute the apples

 

now put the 3 oranges in a row (the new stars) Us bars to divide them into  3 piles, you will need 2 bars.

So you have 5C2 = 10 ways to distribute them

 

20*10 = 200 ways

 
 Oct 9, 2021
 #2
avatar+187 
+1

Thank You Melody

 
Jmaster10  Oct 10, 2021

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