Derangements

In an examination, $5$ students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sits on the allotted seat, is

$5$ boys with allotted roll numbers and seat numbers are seated in such a way that no one sits on the allotted seats. The number of ways of such seating arrangement is

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

Find the rank of the word $\mathrm{SUCCESS}$ in the dictionary.

Number of ways in which $4$ objects out of $6$ distinct objects can be deranged are

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

Let $A=\left\{1,2,3,4,5,6,7\right\}$. The number of surjective functions defined from $A$ to $A$ such that $f\left(i\right)=i$ for atleast four values of $i$ from $i=1,2,......,7$ , is

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?

What is the rank of the word "BALL" in a dictionary that contains all permutation of the word "BALL" ?​

Puneet writes letters to his five friends and address the corresponding envelopes. If $\lambda$ be the numbers of total ways in which the letters can be placed in the envelopes so that at least three of them are in the wrong envelopes, then the value of $\lambda -100$ is 

The letters of the word "GOPAL" are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary, then the rank of the word "GOPAL" is

$10$ people visit a temple. They leave their shoes outside the temple on returning from the temple on they wear the pair, assuming that each person wears both shoes of same pair. Find the number of ways in which exactly 5 person wear their own shoes.

If four letters are placed into 4 addressed envelopes at random, the probability that exactly two letters will go wrong is

If the letters of the word $\mathrm{LATE}$ be permuted and the words so formed be arranged as in a dictionary. Then the rank of $\mathrm{LATE}$ is -

A dictionary is printed consisting of 7 lettered words only that can be made with the letters of word CRICKET. If words are printed in the alphabetic order as in the dictionary then the number of words before the word CRICKET, is -

All the $7$ digits numbers containing each of the $1,2,3,4,5,6,7$ exactly once and not divisible by $5$ are arranged in increasing order. Find ${2015}^{th}$ number in this list?

Let set $A=\{x_1,x_2,x_3,x_4\}$and set  $B=\{y_1, y_2, y_3,y_4\}$. If function is defined from set $A$ to set $B$. Number of one-one function such that $f\left(x_i\right)\ne y_i$ for $i=\mathrm{1,2},\mathrm{3,4}$ is equal to

Number of ways by which $4$ letters can be put in $4$ corresponding envelopes so that all letters go in wrong envelope is

Seven people leave their bags outside a temple and after returning picked one bag each at random. In how many ways at least, one and atmost three of them get their correct bags?

If letters of the word $"KUBER"$ are written in all possible orders and arranged as a dictionary, then rank of the word $"KUBER"$ will be -