Permutations of Alike Things and Repeated Things

Which one of the following responses would be a meaningful order of the given words?

$1$. Imagination
$2$. Sculpture
$3$. Sculpt
$4$. Mud
$5$. Cast

Which of the following will be fourth if they are arranged alphabetically as in the dictionary?

A PSME unit has $10$ ME's, $8$ PME's and $6$ CPM's. If a committee of $3$ members, one from each group is to be formed, how many such committees can be formed?

Which one of the following words will come Second from right if they are arranged according to the dictionary ?

Let $X$  be a set with exactly $5$ elements and $Y$ be a set with exactly $7$ elements. If $\alpha$ is the number of one-one functions from $X$ to$Y$ and $\beta$ is the number of onto functions from $Y$ to  $X$ , then the value of $\frac{1}{5!}\left(\beta -\alpha \right)$ is

There are four hotels in a town. If $3$ men check into the hotels in a day, then what is the probability that each checks into a different hotel$?$

The total number of three-digit numbers, divisible by $3$, which can be formed using the digits $1, 3, 5, 8$, if repetition of digits is allowed, is 

The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is

The number of seven digit numbers using $1,2,3,4$ whose sum of digits is $12$ is

Find the rank of the word $\mathrm{MISSION}$ if all words that can be formed using the letters are arranged in alphabetical order.

Number of ways of arranging the letters of the word $\mathrm{CIRCUMLOCUTION}$ such that it starts with $\mathrm{M}$, $U$ is the successor of $I$ and it ends with $ON$.

If the letters of the word $\mathrm{PAPER}$ are arranged in a dictionary, then the rank of the given word is

A library has $6$ copies of one book, $4$ copies of each of two books, $6$ copies of each of three books and a single copy of each of $8$ books. The number of arrangements of all the books is

If all permutations of the letters of the word MASK are arranged in the order as in dictionary with or without meaning, which one of the following is ${19}^{\mathrm{th} }$ word?

In how many ways can the letters of the word "MULTIPLE" be arranged keeping the position of the vowels fixed?

If all permutations of the letters of the word $MASK$ are arranged in the order as m dictionary with or without meaning, which one of the following is ${19}^{\text{th}}$ word?

The total number of $6$ digited numbers greater than $400000$ that can be formed by using the digits $0, 2, 2, 4, 4, 5$ is

Number of $7$ digit numbers the sum of whose digits is $61$ is:

Let $X$ be the set of all $6-$digit numbers, where all the digits of each number are from the set $\{1,2,3,4,5\}$, and any digit that appears in any one of the numbers appears at least twice (in the same number). Then the number of distinct elements in the set $X$ equals