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Please help me evaluate the following Binomial coefficient using any known properties of Pascal triangle: $$ \binom{52}{4} - \binom{47}{4} + \binom{47}{5} $$

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    Do you have the formula $${n \choose m}=\frac{n!}{m!(n-m)!}~?$$2012-04-19
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    Well, what are the facts about Pascal triangle, you know, what have you tried with them...? @JSSumantri2012-04-19
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    The original problem is $$\binom{47}{5} + \sum_{i=1}^{5}\binom{52-i}{3}$$ Is there any simpler / more elegant way to evaluate the above expression rather than using the factorial formula?2012-04-19
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    @JSSUMANTRI Add the comment to your question, please.2012-04-19

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