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’?

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'?

How many numbers of five digits can be made with the digits 1,2,3 each of which can be used at most thrice in a number?

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 

$7$ people leave their bags outside temple and returning after worshiping the deities picked one bag each at random. In how many ways atleast one and atmost three of them get their correct bags?

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

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?