The number of three-digit numbers in which $9$ appears in exactly one place is

Let $S$ be the set of all passwords which are $6$ to $8$ characters long,where each character is either an alphabet from $\{A, B, C, D, E\}$ or a number from $\{1, 2, 3, 4, 5\}$ with the repetition of characters allowed. If the number of passwords in $S$ whose at least one character is a number from $\{1, 2, 3, 4, 5\}$ is $\alpha \times 5^{6}$,then $\alpha$ is equal to $.......$

The number of all possible combinations of $4$ letters which are taken from the letters of the word $ACCOMMODATION$ is

The number of $9$-digit even natural numbers formed using only the digits $0$ and $1$,such that no two consecutive digits are $0$,is:

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:

$A$ man has $7$ relatives,$4$ of them are ladies and $3$ are gents; his wife has $7$ other relatives,$3$ of them are ladies and $4$ are gents. The number of ways they can invite $3$ ladies and $3$ gents to a party such that there are $3$ of the man's relatives and $3$ of the wife's relatives,is: