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

$\left( {m - 1} \right)\lambda $

$\left( {m + 1} \right)\lambda $

JEE MATHEMATICS MCQ: COMBINATIONS

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Application +4 | -1

If the total number of

m

elements subsets of the set

A = \left\{ {{a_1},{a_2},{a_3}, \ldots {a_n}} \right\}

\lambda

times the number of 3 elements subsets containing

{a_4}

, then

n

View answer and explanation

Correct option: B

m\lambda

Option D (

m\lambda

) is correct because it is derived from the given relationship between the total number of m-element subsets and the number of 3-element subsets containing a specific element.

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{\;^{n + 2}}{C_8}:{\;^{n - 2}}{P_4} = \frac{{57}}{{16}}

, then

n

is equal to