NIMCET 2014 Question Paper with solutions

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Question : 27 of 120

Marks: +1, -0

If n and r are integers such that 1 < r < n, then the value of

n(\,↖{n-1}C_{r-1})

is

$↖{n}C_r$
r ( $↖{n}C_r$ )
n ( $↖{n}C_r$ )
(n - 1) ( $↖{n}C_r$ )

Solution:

We have,

n^{n-1}C_{r-1}

= n

(n-1)/{(r-1)!(n-1-r+1)!}

=

{n!}/{(r-1)!(n-r)!}

=

{r.n!}/{r.(r-1)!(n-r)!}

=

{r.n!}/{r!(n-r)!}

= r .

(\,↖{n}C_r)

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