Looks like Alokananda is a special person here that she has her own annual birthday thread. Who is she? Is she the admin here? I have no clue.

She is a special person for me.

]]>Please remind me a few days before. I have a bad memory for personal dates and I do not want to miss any.

]]>There are many birthdays celebrated here, Agnishom, anonimnystefy, ganesh, mine and several others. Anyone who mentions their birthday will have it celebrated.

I am June 24th, then.

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Oops!

how do I compute the last three digits of 2014C1+2014C3+2014C5+...+2014C2013 by hand?

Consider the question: In how many ways can you select things from a collection of 2014 things?

This is equivalent to 2014C1 + 2014C2 + 2014C3 + .. 2014C2014

For each doll you have, 2 choices. To select it or not, so there are 2^2014 ways.

Now, for only odd number of dolls:

Half of those cases we selected odd number of dolls

This is equivalent to asking in how many cases you are choosing the odd terms.

Clearly the answer is 2^2013

bobbym wrote:

]]>Algebra is Combinatorics, Combinatorics is Algebra