SOLUTION: Father has two apples, three pears, and two oranges. Every morning, during one week, he gives one fruit to his son for breakfast. How many ways are there to do this?

Question 1120023: Father has two apples, three pears, and two oranges. Every morning, during one week, he gives one fruit to his son for breakfast. How many ways are there to do this?

Answer by ikleyn(52875) (Show Source): You can put this solution on YOUR website!
.

Since the condition does not state an opposite, I should assume that the apples are not distinguishable, same as the pears and the oranges.


So we have permutations of 7 fruits with 2 indistinguishable apples, 3 indistinguishable pears and 2 indistinguishable oranges.


The number of distinguishable arrangements is


     =  =  210.


Answer.  There are 210 ways to do it.

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On this subject, see the lesson
- Arranging elements of sets containing indistinguishable elements
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Combinatorics: Combinations and permutations".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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