Permutation

In how many ways can five persons be seated in a row?

How many $3-$digit numbers can be formed by using the digits $1$ to $9$, if  no digit is repeated?

Six candidates are called for interview to fill some vacant posts in an office. Assuming that each candidate is fit for each post, determine the number of ways in which four posts can be filled.

How many $3-$digit numbers can be formed from the digits $1, 2, 3, 4$ and $5$, if repetition of digits is not allowed?

Find the value of $P(4, 3)$.

If the letters of the word $\mathrm{MASTER}$ are permuted in all possible ways and the words thus formed are arranged in dictionary order, then find the rank of the word $\mathrm{MASTER}$.

Find the number of ways of preparing a chain with $6$ different coloured beads.

A round table conference is attended by $3$ Indians, $3$ Chinese, $3$ Canadians and $2$ Americans. Number of ways of arranging them at the round table so that delegates belonging to same country sit together is 

If ${}^{12}{P}_r{=}^{11}{P}_6+6{\times }^{11}{P}_5$, then $r$ is equal to

How many $6$-digit numbers can be formed from the digits $0,1,3,5,7$ and $9$ which are divisible by $10$ and no digit is repeated?

How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if

           $C_1$                                                                            $C_2$

$\left(a\right)$ $4$ letters are used at a time                                         $\left(\mathrm{i}\right)$ $720$ 
$\left(b\right)$ All letters are used at a time                                       $\left(\mathrm{ii}\right)$ $240$
$\left(c\right)$ All letters are used but the                                          $\left(\mathrm{iii}\right)$ $360$
first is a vowel