Five students are selected from n students su | vedclass

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Question

(C) Total students to be selected $= 5$. Total students available $= n$. Number of ways in which $2$ particular students are selected $= {}^{n-2}C_{5-

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(C) Total students to be selected $= 5$. Total students available $= n$. Number of ways in which $2$ particular students are selected $= {}^{n-2}C_{5-2} = {}^{n-2}C_3$. Number of ways in which $2$ particular students are not selected $= {}^{n-2}C_5$. According to the given condition,$\frac{{}^{n-2}C_3}{{}^{n-2}C_5} = \frac{2}{3}$. Using the formula ${}^nC_r = \frac{n!}{r!(n-r)!}$,we have: $\frac{(n-2)!}{3!(n-5)!} 	imes \frac{5!(n-7)!}{(n-2)!} = \frac{2}{3}$ $\frac{5 	imes 4}{ (n-5)(n-6)} = \frac{2}{3}$ $\frac{20}{(n-5)(n-6)} = \frac{2}{3}$ $(n-5)(n-6) = 30$ $n^2 - 11n + 30 = 30$ $n^2 - 11n = 0$ Since $n$ must be at least $7$ (to select $5$ students excluding $2$),$n = 11$.

Five students are selected from $n$ students such that the ratio of the number of ways in which $2$ particular students are selected to the number of ways $2$ particular students are not selected is $2:3$. Then the value of $n$ is

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