In how many ways can the letters of the word '$EXCELLENT$' be arranged?

If $^{12}P_r = 1320$,then $r$ is equal to

The value of $\sum\limits_{r = 0}^{n - 1} {\frac{{^n{C_r}}}{{^n{C_r} + {\,^n}{C_{r + 1}}}}} $ equals

If $n$ is a factor of $72$,such that $xy = n$,then the number of ordered pairs $(x, y)$ is: (where $x, y \in N$)

Find the number of arrangements of the letters of the word '$ALGEBRA$' without altering the relative position of the vowels and the consonants.

There are $m$ men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by $84,$ then the value of $m$ is