1984 AHSME Problem 19

A box contains 11 balls, numbered 1, 2, 3,\ldots,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?

\mathrm{(A) \ }\frac{100}{231} \qquad \mathrm{(B) \ }\frac{115}{231} \qquad \mathrm{(C) \ } \frac{1}{2} \qquad \mathrm{(D) \ }\frac{118}{231} \qquad \mathrm{(E) \ } \frac{6}{11}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.