Discrete Math

Question

5 member commities are to be formed out of 10 people. The names are written in chits of paper and put into 6 boxes. Atleast _______ chits go into the same box.

Answer 1

$10 \choose 5$ will give you the number of ways forming a committee. 

If they have to be put in $6$ boxes, each box will have at least $\lceil\frac{10 \choose 5}{6}\rceil$ chits, which is a direct consequence of the pigeonhole principle.

For a similar question, refer here: https://gateoverflow.in/78071/made-easy-how-many-chits-will-go-into-the-same-box

Comments

ceil or floor?

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Check this:

https://math.stackexchange.com/questions/1537931/pigeonhole-principle-floor-versus-ceiling/1537939