SOLUTION: A gambler places a bet on a horse race. To win, he must pick the top three finishers in any order. Thirteen horses of equal ability are entered in the race. Assuming the horses

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Question 1192983: A gambler places a bet on a horse race. To win, he must pick the top three finishers in any order. Thirteen horses of equal ability are entered in the race. Assuming the horses finish in a random order, what is the probability that the gambler will win his bet?
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

Of the total possible   C%5B13%5D%5E3 = %2813%2A12%2A11%29%2F%281%2A2%2A3%29 = 286   different triples only one wins.

So the probability for the gambler to win is   1%2F243.             ANSWER


Solved.

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This problem is on  COMBINATIONS.

On  Combinations,  see introductory lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Combinatorics: Combinations and permutations".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.