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7 identical apples and 13 identical oranges are to be arranged in a circle so that no two apples are consecutive. No.of ways of doing it is?

I do know about circular permutations and clockwise, anticlockwise arrangements but here the apples and oranges are identical .

PrincessEev
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RUTAN GALENO
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  • This is analogous to this similar question. See also the linked and related questions there. You are looking for the number of 7-sided polygons formed from the vertices of a 20-sided polygon with no sides common. – Daniel Mathias Mar 09 '19 at 14:31
  • Try modifying my solution to this related question. The principal difference between the problems is that boys and girls are distinct while fruits of the same type are treated as identical in this problem. – N. F. Taussig Mar 10 '19 at 10:42

1 Answers1

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Hint:

There must at least be one orange between two apples. As a result, we must use $7$ apples and $7$ oranges (circular permutation).

How many spots are there left for the $6$ remaining oranges? Therefore how many combinations are there?

Toby Mak
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