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in Binomial Theorem by (51.0k points)

If (1 + x)n = C0 + C1x + C2x2 +..........+ Cnxn, then the sum of the products of the Ci’s taken two at a time represented by \(\sum \sum C_iC_j (0\le i<j\le n)\) is equal to

(a) 22n–1

(b) \(2^n - \frac{(2n)!}{2(n!)^2}\)

(c) \(2^{2n-1} - \frac{(2n)!}{2(n!)^2}\)

(d) None of these

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1 Answer

+1 vote
by (51.3k points)

Correct option is (c) \(2^{2n-1} - \frac{(2n)!}{2(n!)^2}\)

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