The number of four-digit numbers that can be formed using all the digits from $1$ to $9$ (excluding zero) such that every number has exactly $2$ distinct digits is:

$A$ committee of $12$ members is to be formed from $9$ women and $8$ men. The number of committees in which the women are in majority is

At an election,a voter may vote for any number of candidates,not greater than the number to be elected. There are $10$ candidates and $4$ are to be selected. If a voter votes for at least one candidate,then the number of ways in which he can vote is:

The number of ways in which $3$ identical balls can be distributed into $7$ distinct bins is

In a Mathematics examination,there are $20$ questions of equal marks. The question paper is divided into three sections: $A, B$,and $C$. $A$ student is required to attempt a total of $15$ questions,taking at least $4$ questions from each section. If section $A$ has $8$ questions,section $B$ has $6$ questions,and section $C$ has $6$ questions,then the total number of ways a student can select $15$ questions is:

Let $S = \{1, 2, 3, \ldots, 9\}$. For $k = 1, 2, \ldots, 5$,let $N_k$ be the number of subsets of $S$,each containing five elements out of which exactly $k$ are odd. Then $N_1 + N_2 + N_3 + N_4 + N_5 =$