SOLUTION: In a lottery game, a machine has 51 balls marked with numbers from 1-51 and six of them are taken out at random. A player picks six of these numbers, trying to match the six balls

Question 1187195: In a lottery game, a machine has 51 balls marked with numbers from 1-51 and six of them are taken out at random. A player picks six of these numbers, trying to match the six balls that come out of the machine in any order. If exactly 4 of those 6 numbers match those drawn, the player wins third prize. What is the probability of winning this prize?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
(6/51)(5/50)(4/49)(3/48)(45/47)(44/46)*15, the 15 is 6C4, the number of different ways 4 can be chosen from 6.
That probability is 0.000825.
Alternatively it is (6C4*45C2)/51C6.
Note how the top part of the terms add up (they are not numerators) to the top part of the denominator and the same with the bottom.

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