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.