From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is $' M '$, is :

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?

A committee of $3$ persons is to be constituted from a group of $2$ men and $3$ women. In how many ways can this be done? How many of these committees would consist of $1$ man and $2$ women?

The number of ways in which $21$ identical apples can be distributed among three children such that each child gets at least $2$ apples, is

$^n{C_r}{ + ^{n - 1}}{C_r} + ......{ + ^r}{C_r}$ =

In how many ways $5$ speakers $S_1,S_2,S_3,S_4$ and $S_5$ can give speeches one after the other if $S_3$ wants to speak after $S_1$ & $S_2$