R D Sharma Solutions for Chapter: Permutations, Exercise 6: VERY SHORT ANSWER QUESTIONS (VSAQs)

Find the total number of ways in which six ‘$+$’ and four ‘$-$’ signs can be arranged in a line such that no two ‘$-$’ signs occur together. (Write only numerical value)

How many arrangements can be made by the letters of the word “$\mathrm{INTERMEDIATE}$” so that vowels always occupy even places of the word.
 

How many arrangements can be made by the letters of the word “$\mathrm{INTERMEDIATE}$” so that the relative order of vowels and consonants do not alter?

The letters of the word $‘\mathrm{ZENITH}’$ are written in all possible orders. How many words are possible if all there words are written out as in a dictionary? 

The letters of the word $‘\mathrm{ZENITH}’$ are written in all possible orders. What is the rank of the word $‘\mathrm{ZENITH}’$?

In how many ways can $4$ letters be posted in $5$ letter boxes?

Write the number of $5$ digit numbers that can be formed using digits $0,1$ and $2$.

In how many ways$4$ women draw water from $4$ taps, if no tap remains unused? (Write only numerical value)