SOLUTION: In a lottery game, a player picks six numbers from 1 to 38. If 5 of the 6 match the winning numbers, then the player wins the second prize. What is the probability of winning the s

Question 1201891: In a lottery game, a player picks six numbers from 1 to 38. If 5 of the 6 match the winning numbers, then the player wins the second prize. What is the probability of winning the second prize?

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
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In a lottery game, a player picks six numbers from 1 to 38. If 5 of the 6 match the winning numbers,
then the player wins the second prize. What is the probability of winning the second prize?
~~~~~~~~~~~~~~~~~~~~~~~~

Usually in such problems, the authors point that repeating of numbers is not allowed.

It is a NECESSARY condition for such problems to be realistic.

It is when the authors do understand the meaning of such problems.

When the authors do not understand the meaning of what they invent,
then their posts becomes simply "soup of words": each word is correct,
but taken altogether, they produce nonsense.

My impression is that at this forum, the other side started to use the artificial intelligence
to create new problems, but in very old, outdated, stupide and far from to be perfect version,
producing an absurd practically at every trial.

Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

The number of ways to choose 6 of the 38 numbers is, literally "38 choose 6":

C(38,6) = 2760681

To win a second prize, you need to get 5 of the 6 winning numbers and 1 of the other 32 numbers:

C(6,5)*C(32,1) = 6*32 = 192

The probability of winning a second prize is

192/2760681 = 64/920227

ANSWER: 64/920227, or about 0.0000695

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