Q59 / 155 · WBJEE 2020 · Mathematics

If the total number of m-element subsets of the set $\mathrm{A}=\left\{\mathrm{a}{1}, \mathrm{a}{2}, \ldots . \mathrm{a}{\mathrm{n}}\right\}$ is $\mathrm{k}$ times the number of $\mathrm{m}$ element subsets containing $\mathrm{a}{4}$, then $\mathrm{n}$ is

A
$(m-1) k$
Correct answer
B
$\mathrm{mk}$
C
$(m+1) k$
D
$(m+2) k$

Solution

Hint: $n_{c_{m}}=k^{n-1} c_{m-1} \Rightarrow n=m k$

Hence, the correct answer is option: 'B'.

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