The number of natural numbers less than $10000$ which are divisible by $5$ and in which no digit is repeated is:

The number of $5$ digit telephone numbers having at least one of their digits repeated is

If ${}^n C_{r-1}=36$, ${}^n C_r=84$, and ${}^n C_{r+1}=126$, then the value of ${}^n C_8$ is

$A$ certain question paper contains three parts $A, B, C$ with four questions in part $A$,five questions in part $B$,and six questions in part $C$. $A$ student is required to answer seven questions,choosing at least two questions from each part. The total number of different ways a student can choose his seven questions for answering is:

The number of ways in which we can select three numbers from $1$ to $30$ such that we exclude every selection consisting of all even numbers is

The number of seven-digit numbers that can be formed by using the digits $1, 2, 3, 5,$ and $7$ such that each digit is used at least once is: