If the total number of $m$ elements 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

Question

Dr. Abubacker · Accepted Answer

(b)
Total number of $m$-elements subsetcs 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, $\ ^{n}C_{m} = \lambda.\ ^{n - 1}C_{m - 1}$
$\Rightarrow \ \frac{n}{m}.^{n - 1}C_{m - 1} = \lambda.^{n - 1}C_{m - 1}\$
$\Rightarrow \ \lambda = \frac{n}{m}\ or\ n = m\lambda$

Q. If the total number of $m$ elements 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

Explanation

Reviewed by Dr. Abubacker

Want more practice?