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The Safe (Posted on 2003-08-11) Difficulty: 2 of 5
A group of crazy bank robbers try to crack a safe, even though they don't have a clue what the code is. The code has 5 numbers in, and the numbers on the dial range from 1 to 60. If they crack the safe, they get 100 billion.(That's a British billion - a million million). If they get the code wrong, they get caught and fined 1 million.

Assuming the bank robbers don't enter the same code twice, if they keep trying and re-trying until they crack the safe, are they more likely to have lost or gained money? If so, how much would they probably gain/lose?

See The Solution Submitted by Lewis    
Rating: 2.7500 (4 votes)

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solution | Comment 4 of 10 |
Any question asking how many ways you can pick a certain number of anything from the whole set of anything (in this case how many ways can you pick 5 different numbers from 60. You use the format 60 choose 5 (on pascal's triangle that is 60 down starting with 0 on the first line and 5 to the left or right starting with 0 on the 1 column.) Algebraically this may be found by 60!/(60-5)!5!=54615120 which means that there is a 1:54615120 chance of getting the right combination. Therefore statistically they need to try it 50% *1 times, to probably get it. Therefore they need to try 27307561 different combinations in order to probably get it. This means that they will probably be fined 27307561000000 pounds. Therefore they will probably make 99999999972692439000000 . The payoff minus the fines. Sorry for such a long solution, I wanted my first one to be a good one.
  Posted by Daniel on 2003-08-11 17:13:20
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