How many words can be formed by using all the letters of the word '$TRIVANDRUM$' using each letter exactly once (in $!$)?

$A$ committee of $11$ members is to be formed from $8$ men and $5$ women. If $m$ is the number of ways to form the committee with at least $6$ men and $n$ is the number of ways to form the committee with at least $3$ women,then:

The number of four-digit numbers strictly greater than $4321$ that can be formed using the digits $0, 1, 2, 3, 4, 5$ (repetition of digits is allowed) is

The number of $6$-digit numbers that can be formed using the digits $0, 1, 2, 5, 7,$ and $9$ which are divisible by $11$ and no digit is repeated,is

From a group of $7$ men and $6$ women,five persons are to be selected to form a committee so that at least $3$ men are there in the committee. In how many ways can it be done?

There are $15$ buses running between Delhi and Mumbai. In how many ways can a man go to Mumbai and return by a different bus?