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

How many words of $4$ distinct letters can be formed using the letters of the word $DHOLPUR$ such that $L$ and $P$ are always included?

If ${ }^{15} C_4+{ }^{15} C_5+{ }^{16} C_6+{ }^{17} C_7+{ }^{18} C_8={ }^{19} C_{r}$,then the value of $r$ is equal to

$A$ student is to answer $10$ out of $13$ questions in an examination such that he must choose at least $4$ from the first $5$ questions. The number of choices available to him is

Determine the number of $5$-card combinations out of a deck of $52$ cards if each selection of $5$ cards has exactly one king.

If ${ }^{n} C_{12}={ }^{n} C_{8}$,then $n$ is equal to