Latest Hexaware Aptitude Question SOLUTION: In how many ways can you distribute 6 prizes among 5 children if every child must get atleast one?

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In how many ways can you distribute 6 prizes among 5 children if every child must get atleast one?

Asked In Hexaware Subhrangsu Bhowmik (12 years ago)

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Shiv Kumar  (12 years ago)

5 Prizes can distribute to 5 children by 5! ways
6 prize (last prize) can be given to any one of child. So there are 5 ways to distribute the sixth gift among 5 children.

So the total no.of ways are 5!+5 = 120+5 = 125 Ways

Is this solution Helpfull? Yes (56) | No (18)  

pravas patra  (10 years ago)

n items can be distributed among r person such that r>=1 in (n-1)C(r-1) ways >>
here n=6,r=5>> ans=5C4=5 ways.....(right answer)

Is this solution Helpfull? Yes (18) | No (4)  

Pargat Pal Singh  (12 years ago)

5 Prizes can distribute to 5 children by 5! ways
6 prize (last prize) can be given to any one of child. So there are 5 ways to distribute the sixth gift among 5 children.

So the total no.of ways = 5* 5! = 120*5 = 600

Is this solution Helpfull? Yes (9) | No (37)  

mini agrawal   (11 years ago)

5 because when each student have atleast one prize and only one prize is left and it can only be given to 5 student in 5 ways

Is this solution Helpfull? Yes (9) | No (14)  

Adarsha dash  (9 years ago)

6 prizes can be distributed to 5 students - 6 * 5*4*3*2 .... This question is same as , how many 5 digit numbers u can make using 6 digitis(repetation not allowed) .. So the answer is 720

Is this solution Helpfull? Yes (5) | No (11)  

Payal Prajapati  (10 years ago)

6^5
there are 5 ways of distributing 6 prizes among 5 children so 6*6*6*6*6 = 6^5

Is this solution Helpfull? Yes (4) | No (16)  

Akshay Suchdeep  (2 years ago)

This can be found by calculating the reverse case.
That is we calculate the number ways of prize distribution in which all prizes are given to any one person.
No. of ways of doing this = 5C1
And total number of ways of prize distribution = 5×5×...×5 = 5^6
So the answer = 5^6 - 5C1 = 5^6 - 5 = 15620

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