If $\binom{189}{35} + \binom{189}{x} = \binom{190}{x}$,then $x = \dots$

In how many ways can a committee consisting of one or more members be formed out of $12$ members of the Municipal Corporation?

If $n$ and $r$ are two positive integers such that $n \ge r,$ then $^nC_{r-1} + ^nC_r = $

The total number of ways of selecting $4$ letters from all the letters of the word $TSEAMCET$ is

$A$ group of $9$ students,$s_1, s_2, \ldots, s_9$,is to be divided into three teams $X, Y$,and $Z$ of sizes $2, 3$,and $4$,respectively. Suppose that $s_1$ cannot be selected for team $X$,and $s_2$ cannot be selected for team $Y$. The number of ways to form such teams is:

If ${}^n C_r$ denotes the number of combinations of $n$ things taken $r$ at a time,then the expression ${}^n C_{r+1} + {}^n C_{r-1} + 2{}^n C_r$ equals