How many different ways can the letters in the word $ATTEND$ be arranged?

There are $10$ persons named $A, B, \dots, J$. We have the capacity to accommodate only $5$. In how many ways can we arrange them in a line if $A$ must be included and $G$ and $H$ must not be included in the team of $5$?

How many $3$-digit numbers,each less than $600$,can be formed from the digits $1, 2, 3, 4, 5,$ and $9$,if repetition of digits is allowed?

The letters of the word $MODESTY$ are written in all possible orders and these words are written out as in a dictionary,then the rank of the word $MODESTY$ is

How many three-digit numbers can be formed from the digits $2, 3, 5, 6, 7,$ and $9$ which are divisible by $5$,given that no digit is repeated?

The number of ways in which $5$ male and $2$ female members of a committee can be seated around a round table so that the two female are not seated together is