If the letters of the word $SACHIN$ are arranged in all possible ways and these words are written out as in a dictionary,then the word $SACHIN$ appears at serial number:

In how many ways can a team of $10$ players be selected from $22$ players if $6$ particular players are always to be included and $4$ particular players are always excluded?

$A$ lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends,if two of the friends will not attend the party together is

There are $n$ points in a plane of which $p$ points are collinear. How many lines can be formed from these points?

If $\frac{{}^{n + 2}{C_6}}{{}^{n - 2}{P_2}} = 11$,then $n$ satisfies the equation

$A$ man $X$ has $7$ friends,$4$ of them are ladies and $3$ are men. His wife $Y$ also has $7$ friends,$3$ of them are ladies and $4$ are men. Assume $X$ and $Y$ have no common friends. The total number of ways in which $X$ and $Y$ together can throw a party inviting $3$ ladies and $3$ men,such that $3$ friends of each of $X$ and $Y$ are in this party,is: