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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?

How many numbers greater than $100$ and divisible by $5$ can be made from the digits $3, 4, 5, 6$,if no digit is repeated?

There are $11$ distinct books on a shelf,consisting of $5$ Mathematics,$4$ Physics,and $2$ Chemistry books. In how many ways can they be arranged such that books of the same subject are always kept together?

The number of integers greater than $3000$ that can be formed by using any number of digits from the set $\{0, 1, 2, 3, 4, 5\}$ without repetition is:

There are $6$ periods in each working day of a school. The number of ways one can arrange $5$ subjects such that each is allowed at least one period is:

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