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BMAT 2018 · Question 18 · Logic

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Three-year old Arthur has a junior skittles set. It contains four red skittles, four yellow skittles, three balls and a felt mat. The mat is shown below. Six of the eight skittles are placed on the spots (there are two extra in the set in case of loss or damage). The balls must then be bowled from behind the line at the other end of the mat.

Question diagram

How many different arrangements of red and yellow skittles are possible on the six circles on the mat?