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Contributing Member
race
A race is going on. 5 persons participating the race.
In how many ways the participants cross the finishing line including ties ?
(For Example, if 2 people participating then there are three ways to finish the race.
1. first person win, second runner
2. second person win, first runner
3. both of them finished at the same time ie. tie )
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suresh
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Expert Member
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Expert Member
Re: race
sorry my answer is wrong!!
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Expert Member
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Contributing Member
Re: race
no smart coder....it's also wrong..
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suresh
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Expert Member
Re: race
i know...i miscalculated!!
i m working on P&C
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Expert Member
Re: race
i think the ans should be, though not sure
135
right?
bye
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Expert Member
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Contributing Member
Re: race
hi smart coder,
541 is the correct answer...leave your solution here...
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suresh
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Expert Member
Re: race
ok..its a detailed solution...i used P&C ..but did some mistakes earlier but finally got correct solution
Its a long solution
I would break the solution in 5 parts
part1: Only first position is secured(1st)
This means all sprinters reached finished line at the same time
there could be only 1 way for this
part2: Only two position secured(1st and 2nd)
5c1 + 5c2 + 5c3 + 5c4 = 30
part3: Only three position secured(1st ,2ndand 3rd)
5c1(4c1+4c2+4c3) + 5c2(3c1+3c2) + 5c3(2c1) = 150
part4: Only four position secured(1st ,2nd, 3rd and 4th)
5c1[4c1(3c1 + 3c2) + 4c2(2c1)] + 5c2[3c1(2c1)] = 240
part5: All positions secured
5! = 120
1+30+150+240+120 = 541
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