Question

I need help with this question...

there are 9 counters in a bag. there is a number on each counter.
the counters are: 1,1,2,2,2,3,3,3,3
kal takes at random 3 counters from the bag. he adds together the numbers on the 3 counters to get his total. work out the probability that his total is 6.

Answer 1

there are 2 ways to get 6 by withdrawing 3 counters:

1,2 and 3

and 2, 2 and 2.

Probability ( drawing 1 , 2 and 3 in that order) = 2/9 * 3/8 * 4/7 = 24/504 = 1/21

there are 6 ways to draw any combination of 1,2 and 3 so this gives

6 * 1/21 = 2/7

probability of drawing 2,2 and 2 = 3/9 * 2/8 * 1/7 = 1/84

so the answer is 2/7 + 1/84 = 25/84