A) \[(m-1)\,\lambda \]
B) \[m\lambda \]
C) \[(m+1)\,\lambda \]
D) \[0\]
Correct Answer: B
Solution :
Total number of m elements subsets of \[A{{=}^{n}}{{C}_{m}}\]and number of m elements subsets of A each containing the element \[{{a}_{4}}{{=}^{n-1}}{{C}_{m-1}}\] According to question, \[^{n}{{C}_{m}}=\lambda \cdot {{\,}^{n-1}}{{C}_{m-1}}\] \[\Rightarrow \] \[\frac{n}{m}\cdot {{\,}^{n-1}}{{C}_{m-1}}={{\lambda }^{n-1}}{{C}_{m-1}}\] \[\Rightarrow \] \[\lambda =\frac{n}{m}\,\,\Rightarrow \,\,\,n=m\lambda \]
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