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

Is it 14521??

sorry my answer is wrong!!

the answer is 285

no smart coder....it's also wrong..

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suresh

i know...i miscalculated!!
i m working on P&C

i think the ans should be, though not sure

135


right?

bye

is it 541??

hi smart coder,

541 is the correct answer...leave your solution here...

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suresh

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