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  • If the total number of  element subsets of the set <img alt="A=\left\{a_1, a_2, a_3, \ldots, a_n\right\}" src="

If the total number of m element subsets of the set A=\left\{a_1, a_2, a_3, \ldots, a_n\right\} is \lambda times the number of 3 elements subsets containing a_4, then n is 

Option: 1

(m-1) \lambda


Option: 2

m \lambda


Option: 3

(m+1) \lambda

 


Option: 4

0


Answers (1)

best_answer

Total number of m- elements subsets of A={ }^n C_m\: \: \: \: \: \: ...(i)

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}

\begin{aligned} \Rightarrow & & \frac{n}{m} \cdot{ }^{n-1} C_{m-1} & =\lambda \cdot{ }^{n-1} C_{m-1} \\ \Rightarrow & & \lambda & =\frac{n}{m} \\ & \text { or } & n & =m \lambda \end{aligned}

Posted by

Suraj Bhandari

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