SOLUTION: In a certain lottery, three numbered balls are randomly drawn from a large basket without replacement. To win, a player's ticket must have each of the numbers drawn in no particula

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Question 1139615: In a certain lottery, three numbered balls are randomly drawn from a large basket without replacement. To win, a player's ticket must have each of the numbers drawn in no particular order. The balls are numbered from one to one hundred. If Jack buys twenty-four tickets, what is the probability that he will win?
Found 2 solutions by VFBundy, ikleyn:
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
Chances of winning with one ticket:

3/100 * 2/99 * 1/98 = 1/161700

Chances of NOT winning with 24 tickets:

(161699/161700)^24 = 0.99985

Therefore, Jack's chances of winning with 24 tickets is: 1 - 0.99985...or 0.00015. That's about a 1 in 6667 chance.

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

            In my post, I'd like to propose another solution. 


We have 100 balls numbered from 1 to 100, inclusively; so we have 100 distinguishable balls.


Of them, we can form  C%5B100%5D%5E3 = %28100%2A99%2A98%29%2F%281%2A2%2A3%29 = 161700 different triples.


Jack's 24 tickets cover 24 such triples - so the probability to win for Jack is 


    24%2F161700 = 0.000148 = 0.0148%  (approximately).     ANSWER