SOLUTION: In a lottery game, a player picks six numbers from 1 to 48. If 4 of those 6 numbers match those drawn, the player wins third prize. What is the probability of winning this prize?

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Question 1150222: In a lottery game, a player picks six numbers from 1 to 48. If 4 of those 6 numbers match those drawn, the player wins third prize. What is the probability of winning this prize?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

The idea of the solution is vary simple.


First, we should calculate the number of all possible groups of 6 numbers, selected from  48 numbers.

      This number is  C%5B48%5D%5E6 = %28%2848%2A47%2A46%2A45%2A44%2A43%29%2F%281%2A2%2A3%2A4%2A5%2A6%29%29 = 12271512.



Next we should calculate the number of all possible groups ot 6 numbers, that contain 4 particular numbers.

      This numbers is  C%5B44%5D%5E2 = %2844%2A43%29%2F2 = 946


(since we can combine any of 2 remained 48-4 = 44 numbers with 4 particular numbers).



Finally, the desired probability is the ratio  P = 946%2F12271512 = 1%2F12972.    ANSWER

Solved.