Evaluate $7!$

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

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

We are to form different words with the letters of the word $INTEGER$. Let $m_1$ be the number of words in which $I$ and $N$ are never together and $m_2$ be the number of words which begin with $I$ and end with $R$,then $m_1/m_2$ is equal to

The number of natural numbers less than $500$ in which no two digits are repeated is

How many $4$-digit odd numbers can be formed using the digits $0, 1, 2, 3, 5, 7$ if repetition of digits is allowed?