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Question

Question: \[\frac{nC_{r}}{nC_{r - 1}} =\]...

nCrnCr1=\frac{nC_{r}}{nC_{r - 1}} =

A

nrr\frac{n - r}{r}

B

n+r1r\frac{n + r - 1}{r}

C

nr+1r\frac{n - r + 1}{r}

D

nr1r\frac{n - r - 1}{r}

Answer

nr+1r\frac{n - r + 1}{r}

Explanation

Solution

nCrnCr1=n!r!(nr)!n!(r1)!(nr+1)!\frac{nC_{r}}{nC_{r - 1}} = \frac{n!}{\frac{r!(n - r)!}{\frac{n!}{(r - 1)!(n - r + 1)!}}}n!r!(nr)!×(r1)!(nr+1)!n!\frac{n!}{r!(n - r)!} \times \frac{(r - 1)!(n - r + 1)!}{n!}

=(nr+1)(r1)!(nr)!r(r1)!(nr)!=\frac{(n - r + 1)(r - 1)!(n - r)!}{r(r - 1)!(n - r)!} = (nr+1)r\frac{(n - r + 1)}{r}.