How many permutations can be made by using all the letters of the word $MATHEMAGICA$?

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

Find the number of ways in which two Americans,two British,one Chinese,one Dutch,and one Egyptian can sit at a round table so that persons of the same nationality are separated.

Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1} - T_n = 10$,then the value of $n$ is:

$6$ boys and $5$ girls sit in a line such that $(I)$ no two girls sit together $(II)$ all the girls sit together. If $p$ is the number of arrangements in case $(I)$ and $q$ is the number of arrangements in case $(II)$,then $p/q =$

In how many ways can a garland be made from exactly $10$ flowers?