[SOLVED] Combinatorics

let's start warming up with a problem in combinatorics you can find the question (level: undergraduate) in the following link
uploading.com Combinatorics.pdf/

I'll post the solution next week. At the moment no prize, I should evaluate you at first then you will see how much I am generous .

Hey Mohammad! The link doesn't work You have to link directly to the PDF file!

Hello Mohammad

Now the link works. And here is my solution!

If you have a combinatorial proof I'd love to see it. I tried going down that path at first but it did not seem like the best plan.

Well done, your proof is the same I had in my mind.
Now I should be careful who I am talking to

Thanks! I don't know if there is another good way to do it. This seems like the only straightforward solution.

It's funny because last night I was trying all sorts of stupid things for about thirty minutes (even induction! ) , then I got discouraged and I went to take a nap before going to a party. I woke up thirty minutes later and my first thought was "Chebyshev inequality", and I was so certain it would work that I didn't even check until this morning!