Probability of picking 1st ball = 6 / 49 Probability of picking 2nd ball = 5 / 48 Probability of picking 3rd ball = 4 / 47 Probability of picking 4th ball = 3 / 46 Probability of picking 5th ball = 2 / 45 Probability of not picking 6th ball = 43 / 44 This gives 6x5x4x3x2x43 / 49x48x47x46x45x44 However, the ball we failed to pick could also have been 1st, 2nd, etc. so we need to multiply this probability by 6. Multiply the result by 13,983,816 and you get 258 Or looked at another way, you have six chances to pick the wrong ball and in each of those cases there are 43 possible values for it and 6 x 43 = 258 My head hurts! :D