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(B) The total number of $m$-element subsets of a set with $n$ elements is given by $\binom{n}{m}$.The number of $m$-element subsets containing a speci

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$mk$

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(B) The total number of $m$-element subsets of a set with $n$ elements is given by $\binom{n}{m}$.The number of $m$-element subsets containing a specific element $a_{4}$ is equivalent to choosing the remaining $(m-1)$ elements from the remaining $(n-1)$ elements, which is $\binom{n-1}{m-1}$.According to the problem, $\binom{n}{m} = k 	imes \binom{n-1}{m-1}$.Using the identity $\binom{n}{m} = \frac{n}{m} \binom{n-1}{m-1}$, we have:$\frac{n}{m} \binom{n-1}{m-1} = k \binom{n-1}{m-1}$.Dividing both sides by $\binom{n-1}{m-1}$ (assuming $n \ge m \ge 1$), we get:$\frac{n}{m} = k \Rightarrow n = mk$.

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

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