Doubt in n repeated Bernoulli trials

[jman...@gmail.com]

Hi,

I have a question about what is happening in this video at 00:02:27 -

http://www.youtube.com/watch?v=ejbPM1ehP0A#t=147s.

I have this doubt in the previous video also. Here our sample space is {1,2,...,n}, where each k in S represent the k successes in the n-tuple. So k is a set containing n-tuples with all of them having exactly k successes. I don't understand why the cardinality of this set is nCk. nCk is basically the number of groups of k candidates tht can be made out of n candidates. In our case, out of n candidates, k are successes and n-k are failures. I don't understand like how nCk ensures the cardinality of this set. May you please explain..

Thanks!

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Reference Key - Key('StudentQuestionEntity', 4509867812323328, namespace='ns_noc21_ma31')

[Vinay M]

I think it's simple, we have n trials out of which k are successes and rest n-k are failure, the cardinality of a set which has exactly k successes out of n is nothing but n choose k because the successes and failures can be arranged in different places along n trials.