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bmat question

three year old Arthur has a junior skittles set. it contains four red skittles, four yellow skittles, three balls and a felt mat.

six of the eight skittles are placed on the spots (there's two extra in case of loss or damage). the balls must then be bowled from behind the line at the other end of the mat .

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

the answer is 50 but I rlly just need someone to explain how to get there please. I can kind of understand it but if I got another question similar to this I don't think I'd be able to answer it. thank u

Reply 1

Raksha02

Original post by hadeel.

You have to consider three possibilities:

Having 2 red and 4 yellow, 3 red and 3 yellow and 4 red and 2 yellow in your six spots.

For the first and third scenarios it is 6!/(4!*2!), and we have to divide by the 4 and 2 factorials to account for repetition. This gives 15 possibilities for each and a total of 30.

Then for the second it is 6!/(3!*3!) = 20.

That is a total of 50