How many words,with or without meaning,each of $3$ vowels and $2$ consonants can be formed from the letters of the word $INVOLUTE$?

There are $15$ stations on a railway line. How many different types of tickets must be printed so that a passenger can travel from any station to any other station?

If $a$ denotes the number of permutations of $(x + 2)$ items taken all at a time,$b$ denotes the number of permutations of $x$ items taken $11$ at a time,and $c$ denotes the number of permutations of $(x - 11)$ items taken all at a time. If $a = 182bc$,find the value of $x$.

The number of four-digit numbers that can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ which are divisible by $3$,when repetition of digits is allowed any number of times,is

There are $4$ parcels and $5$ post-offices. In how many different ways can the registration of the parcels be made?

How many arrangements of the letters of the word $SALOON$ are there,such that the two $O$'s do not come together?