How many different distinguishable horizontal arrangements of 7 identically shaped balls are there if 2 are blue, 3 are red, and 2 are yellow?

1 Answer
MeneerNask
Sep 30, 2016

If the balls were all different (B1,B2,R1,R2,R3,Y1,Y2) we have:
#7xx6xx5xx4xx3xx2xx1=5040# possibilities

Explanation:

But B1-B2 willl look the same as B2-B1, so we have to divide by #2#.
For the same reason we have to divide by #2# for the yellow balls.
The red balls may be in #3xx2xx1=6# orders.

Summary :
#N=5040/(2xx6xx2)=210#

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