The number of ways of arranging all the letters of the word "$SUNITHA$" so that the vowels always occupy the first,middle,and last places is

In how many ways can the letters of the word "$ASSASSINATION$" be arranged so that all $S$'s are together?

How many $5$-digit telephone numbers can be constructed using the digits $0$ to $9$ if each number starts with $67$ and no digit appears more than once?

There are $3$ applicants for a scholarship in Physics,$5$ for Mathematics,and $4$ for Chemistry. In how many different ways can these scholarships be awarded such that at least one scholarship is awarded in each subject?

In a class of $20$ students,in how many ways can the following prizes be awarded?
If the first and second prizes are for Mathematics,the first and second prizes for Physics,the first prize for Chemistry,and the first prize for English are to be awarded.

If the letters of the word $MATHS$ are permuted and all possible words so formed are arranged as in a dictionary with serial numbers,then the serial number of the word $THAMS$ is