How many numbers between $99$ and $1000$ can be formed using the digits $2, 3, 7, 0, 8, 6$ if each digit is used only once?

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.

All possible four-digit numbers are formed using the digits $0, 1, 2, 3$ such that no digit is repeated. The number of even numbers among them is

If the letters of the word $MOTHER$ are arranged in all possible ways and these words are listed in dictionary order,what is the rank of the word $MOTHER$?

Find the total number of arrangements of the letters of the word $EAMCET$ such that no two vowels are together.

If four-letter words (need not be meaningful) are to be formed using the letters from the word $MEDITERRANEAN$ such that the first letter is $R$ and the fourth letter is $E$,then the total number of such words is