The number of $5$-digit numbers which are divisible by $4$,with digits from the set $\{1, 2, 3, 4, 5\}$ and the repetition of digits is allowed,is . . . . . .

How many ways are there to arrange the letters of the word $EDUCATION$ so that all the following three conditions hold?
- The vowels occur in the same order $(E, U, A, I, O)$.
- The consonants occur in the same order $(D, C, T, N)$.
- No two consonants are next to each other.

How many words,with or without meaning,can be formed using the letters of the word $MONDAY$,assuming that no letter is repeated,if all letters are used but the first letter is a vowel?

The value of $^n{P_r}$ is equal to

Let $P$ be the set of seven-digit numbers with the sum of their digits equal to $11$. If the numbers in $P$ are formed by using the digits $1, 2,$ and $3$ only,then the number of elements in the set $P$ is:

The number of different words that can be formed out of the letters of the word $MORADABAD$ taken four at a time is