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MadeEasy Test Series: Combinatory - Pigeonhole Principle

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A community of 5 members is to be formed out of 10 people. The names are written in chits of paper and put into 6 boxes. So how many chits will go into the same box?

 

Anyone, please make me understand this question.
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This question basically uses Pigeon Hole Principle and combination(selection) formula.According to pigeon hole principle :

If  we have m objects and n holes , then we can say at least ceil(m/n) objects will be allocated the same hole.

So the keywords to look into for such problems are "at least how many" and "same location or same box etc"

So now to calculate number of objects which is number of chits possible here each of which comprises of 5 names to be selected out of 10 persons.

So no of chits   =   No of ways of selecting 5 persons from 10 persons

                       =   10C5

                       =   (10 * 9 * 8 * 7 * 6) / 120

                       =   252

So  we have value of m in this context = 252

And no of holes given which is no of boxes in this case  =  6

So no of chits which will go to same box   =  ceil(252 / 6)

                                                             =   42

Hence at least 42 chits will go into same box.

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