How many words can be formed with the letters of the word $MATHEMATICS$ by rearranging them?

All the letters of the word $LETTER$ are arranged in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order. Then the rank of the word $TETLER$ is

Find the number of arrangements of the letters of the word $INDEPENDENCE$. In how many of these arrangements do the words begin with $I$ and end in $P$?

The number of integers greater than $6000$ that can be formed by using the digits $0, 5, 6, 7, 8,$ and $9$ without repetition is

How many $3$-digit even numbers can be formed using the digits $1, 2, 3, 4, 6, 7$,if no digit is repeated?

Ten chairs are numbered as $1$ to $10$. Three women and two men wish to occupy one chair each. First,the women choose the chairs marked $1$ to $6$,then the men choose the chairs from the remaining. The number of possible ways is