Stars and bars forever

Probability Level 1

There are 5 stars and 4 bars to be arranged in the 9 spaces pictured below. One possible arrangement is shown.

How many possible arrangements are there?


The answer is 126.

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Andy Hayes by Andy Hayes , 38, USA

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2 solutions

Andy Hayes
May 11, 2016

Relevant wiki: Identical Objects into Distinct Bins

There are ( 9 4 ) = 126 \binom{9}{4}=126 ways to choose a location for the bars. After the bars locations are chosen, the stars will fill in the rest. Thus, there are 126 \boxed{126} arrangements of the stars and bars.

17 Helpful 2 Interesting 1 Brilliant 4 Confused

There are 9! Permutations possible , but there are 4 and 5 identical objects (ie .. 4 bars and 5 stars) so , the over all permissions are 9!/(5! *4!) = 9c4 = 126

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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