If((n),(r )) "denotes " ""^nCr then (...

If`((n),(r )) "denotes " ""^nC_r then `
(a) Evalutae : `2^(15)((30),(0))((30),(1))-2^(14)((30),(1))((29),(14))+2^(13)((30),(2))((28),(13)).......-((30),(15))((15),(0))`
( b) Prove that : `Sigma_(r=1)^(n) ((n-1),(n-r))((n),(r))=((2n-1),(n-1))` ( c) Prove that : `((n),(r))((r),(k))=((n),(k))((n-r),(r-k))`

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The correct Answer is:

`((30),(15))`

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