How many words can be formed using the letters of the word $COMMITTEE$?

Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by $66$,then the number of men who participated in the tournament lies in the interval

The straight lines $l_1, l_2, l_3$ are parallel and lie in the same plane. $A$ total number of $m$ points are taken on $l_1$,$n$ points on $l_2$,and $k$ points on $l_3$. The maximum number of triangles formed with vertices at these points is:

$^nC_r + ^nC_{r-1}$ is equal to

If the permutations of $A, B, C, D, E$ taken all together are written down in alphabetical order as in a dictionary and numbered,then the rank of the permutation $DEBAC$ is

$A$ group of students comprises $5$ boys and $n$ girls. If the number of ways in which a team of $3$ students can be selected from this group such that there is at least one boy and at least one girl in each team is $1750$,then $n$ is equal to: