How many words,with or without meaning,can be formed using all the letters of the word $EQUATION$,using each letter exactly once?

Evaluate $8!$.

The number of ways of arranging the letters of the word $BANANA$ so that the two $N$s do not come together is:

Words of length $10$ are formed using the letters $A, B, C, D, E, F, G, H, I, J$. Let $x$ be the number of such words where no letter is repeated,and let $y$ be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then,$\frac{y}{9x} =$

Among the $4$-digit numbers formed using the digits $0, 1, 2, 3, 4$ where repetition of digits is allowed,the number of numbers which are divisible by $4$ is:

If all the words (with or without meaning) having five letters,formed using the letters of the word $SMALL$ and arranged as in a dictionary,then the position of the word $SMALL$ is: