There are 12 counters in a bag. There is an equal number of red counters, yellow counters and blue counters in the bag. There are no other counters in the bag. 3 counters are taken from the bag. Work out the probability of taking 3 red counters.

If there are 12 counters in a bag,each with colour either red, yellow or blue, we can say that the number of red counters, blue counters and yellow counters must add up to 12.R + B + Y = 12 ( R = No. of Red counters, B = No. of Blue counters and Y = No. of Yellow counters)We also know that the number of each colour counter is the same, so,R = B = YIf the number of Red counters is the same as Blue and Yellow thenR + R + R = 12 So now we know 3 x R = 12 and so R = 4,There are 4 red counters in the bag.Now we want the probability of picking 3 red counters from the 12. The probability of picking 1 red is 4/12Since each time we pick a red counter out of a bag there is one less red counter in the bag the probability of picking 2 red counters is 4/12 x 3/11 ( 4->3 because there is one less red, 12 ->11 because one less counter in bag as a whole)Therefore the probability of choosing 3 red counters is (4/12) x (3/11) x (2/ 10) = 1/55