Problem:
A box contains 11 balls, numbered 1,2,3,…,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 Choices:
A. 231100​
B. 231115​
C. 21​
D. 231118​
E. 116​
Solution:
The sum is odd if and only if an odd number of odd numbered balls is chosen. Of the (611​)=462 possible unordered sets of 6,(16​)(55​)=6 have 1 odd numbered ball, (36​)(35​)=200 have 3, and (56​)(15​)=30 have 5. So the probability is (6+200+30)/462=118/231.