Latest TCS Aptitude Question SOLUTION: an elevator starts with 5 passengers and stop with 5 diff floors of an apartment .find the probability of all 5 passengers are of diff floor?

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an elevator starts with 5 passengers and stop with 5 diff floors of an apartment .find the probability of all 5 passengers are of diff floor?

Asked In TCS TargetTCS 2014 (10 years ago)

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rishabh raj  (10 years ago)

ans should be 5!/5^5
sol : as each person can reach a floor in 5 different ways independently .so there are a total of 5^5 ways to reach i.e. sample space.
and to reach at separate floor 1st person can reach in 5 ways,,2nd can in 4 ways,,3rd in 3 ways ,,4th in 2 ways and 5th can in 1 way ...i. e. n(e) = 5!
therefore p(e) = n(e)/sampl space = 5!/5^5

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PAYAL PATTANAYAK  (10 years ago)

when anyone can go on any floor then
1st can go to any floor in n ways.
2nd can go to any floor in n ways.
3rd can go to any floor in n ways.
4th can go to any floor in n ways.
5th can go to any floor in n ways.
so total no. of ways passenger alighting at floors = n*n*n*n*n = n^5

now when they go to different floor then :-
1st can go to any floor in n ways.
2nd can go to any floor in n-1 ways.
3rd can go to any floor in n-2 ways.
4th can go to any floor in n-3 ways.
5th can go to any floor in n-4 ways.
so probabolity required will be = n*(n-1)*(n-2)*(n-3)*(n-4)/n^5

Is this solution Helpfull? Yes (25) | No (1)  

khitish mishra  (10 years ago)

total no. of possible outcomes=5^5=3125
no. of favourable outcomes=5c1*4c1*3c1*2c1*1c1=120
so, p(e)=no. of favourable outcome/total no. of possible outcomes
i.e 120/3125

Is this solution Helpfull? Yes (12) | No (2)  

Guru Pranav  (10 years ago)

Yes, 5!/5^5 is correct answer !!!

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