Question 356933: A box contains eleven balls, numbered 1,2,3….10,11,11. if 6 balls are drawn simultaneously at random, what is the probability that the sum of the numbers on the balls drawn is odd?
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! Breaking down the possibilities:
0 odd, 6 even = sum is even
1 odd, 5 even = sum is odd
2 odd, 4 even = sum is even
3 odd, 3 even = sum is odd
4 odd, 2 even = sum is even
5 odd, 1 even = sum is odd
6 odd, 0 even = sum is even
We only need to consider the odd cases given above
i) 1 odd, 5 even. The number of ways of selecting 1 odd and 5 even is
ii)3 odd, 3 even. The number of ways of selecting 3 odd and 3 even is
iii)5 odd, 1 even. The number of ways of selecting 5 odd and 1 even is
 .
Now the total number of ways of selecting 6 out of 11 balls is  . Therefore the probability that the sum of the numbers on the balls drawn is odd is  . (Since the 3 cases above are mutually exclusive.)
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