Derangements

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

There is a word $\mathrm{CARIHT}$ in the comedy book and if the letters of the word $\mathrm{CARIHT}$ are arranged in all possible ways as listed in dictionary. Then what is the rank of the word $\mathrm{CARIHT}$?

How many different words can be made out of the letters of INVOLUTE so that each word may contain $3$ vowels and $2$ consonants?

How many different algebraic expressions can be made by combining the letters $a,b,c,d$ and $e$ in this order with the signs $\text{'}+\text{'}$ and $\text{'}-\text{'}$ all the letters taken together?

From $3$ capital letters, $5$ consonants and $4$ vowels, all being different, how many words (i.e., arrangements) can be made each containing $3$ consonants, $2$ vowels and beginning with a capital letter?

In how many ways can $4$ letters be selected out of the letters of the ‘EXPRESSION’?

All possible permutations of the word MOTHER are arranged in dictionary order. Find the rank of the word MOTHER.

All possible permutations of the word RANDOM are arranged in dictionary order. Find the rank of the word RANDOM.

If the permutations of the word EXAMINATION are arranged in dictionary order, how many words are then before the first word starting with $\mathrm{E}$?

If all the letters of the word AGAIN be arranged in dictionary order, what is the $50\mathrm{th}$ word?

How many arrangements can be made out of the letters of the word COMMITTEE, taken all at a time, such that the $4$ vowels do not come together?

How many of these words will not contain the two L's together?

In how many ways  can the letter of the word INDEPENDENCE be arranged so that

the words begin with I and end with P?

In how many ways  can the letter of the word INDEPENDENCE be arranged so that

the vowels never occur together ?

In how many ways can the letter of the word INDEPENDENCE be arranged so that the words begin with P?

In how many ways can the letters of the word ARRANGE he arranged so that

neither two A's nor two R's; are together 

The 'cylinder' of a 'Letter-lock' contains $5$ rings. On each ring 6 different letters are engraved. How many unsuccessful attempts may be made to open the lock by a person who does not know the 'key-word'?

There are unlimited number of identical balls of four different colours. How many arrangements of at most $8$ balls in a row can be made by using them?

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