In a high school,a committee has to be formed from a group of $6$ boys $M_1, M_2, M_3, M_4, M_5, M_6$ and $5$ girls $G_1, G_2, G_3, G_4, G_5$.
$(i)$ Let $\alpha_1$ be the total number of ways in which the committee can be formed such that the committee has $5$ members,having exactly $3$ boys and $2$ girls.
$(ii)$ Let $\alpha_2$ be the total number of ways in which the committee can be formed such that the committee has at least $2$ members,and having an equal number of boys and girls.
$(iii)$ Let $\alpha_3$ be the total number of ways in which the committee can be formed such that the committee has $5$ members,at least $2$ of them being girls.
$(iv)$ Let $\alpha_4$ be the total number of ways in which the committee can be formed such that the committee has $4$ members,having at least $2$ girls and such that both $M_1$ and $G_1$ are $NOT$ in the committee together.
$LIST-I$$LIST-II$
$P$. The value of $\alpha_1$ is$1. 136$
$Q$. The value of $\alpha_2$ is$2. 189$
$R$. The value of $\alpha_3$ is$3. 192$
$S$. The value of $\alpha_4$ is$4. 200$
$5. 381$
$6. 461$

The correct option is:

  • A
    $P \rightarrow 4; Q \rightarrow 6; R \rightarrow 2; S \rightarrow 1$
  • B
    $P \rightarrow 1; Q \rightarrow 4; R \rightarrow 2; S \rightarrow 3$
  • C
    $P \rightarrow 4; Q \rightarrow 6; R \rightarrow 5; S \rightarrow 2$
  • D
    $P \rightarrow 4; Q \rightarrow 2; R \rightarrow 3; S \rightarrow 1$

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