SOLUTION: In a lottery game, a player picks six numbers from 1 to 53. If 5 of the 6 numbers matches those drawn, the player wins $1000. What is the probability of winning this prize?

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Question 1162122: In a lottery game, a player picks six numbers from 1 to 53. If 5 of the 6 numbers matches those drawn, the player wins $1000. What is the probability of winning this prize?
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
The player can pick all 6 winning numbers in 6C6 = 1 way
The player can pick 5 winning numbers and 1 non-winning number in (6C5)∙(47C1) = 282 ways.

So there are 1+282=283 ways the player could win.

There are 53C6 = 22957480 ways the player could pick 6 numbers.

Probability of winning = 283 ways out of 22957480 or 283/22957480 or about

0.000012327136950571229943356152330308030323885722649001545...

1.2327×10-5, which is about 1 chance in 81122.

Edwin
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