If $P(n,r) = 1680$ and $C(n,r) = 70$, then $69n + r! = $

In an examination there are three multiple choice questions and each question has $4 $ choices. Number of ways in which a student can fail to get all answers correct, is

$6$ different letters of an alphabet are given. Words with four letters are formed from these given letters. Then the number of words which have atleast one letter repeated and no two same letters are together, is

The number of values of $'r'$ satisfying $^{69}C_{3r-1} - ^{69}C_{r^2}=^{69}C_{r^2-1} - ^{69}C_{3r}$ is :-  

A group of $9$ students, $s 1, s 2, \ldots, s 9$, is to be divided to form three teams $X, Y$ and, $Z$ of sizes $2,3$ , and $4$, respectively. Suppose that $s_1$ cannot be selected for the team $X$, and $s_2$ cannot be selected for the team $Y$. Then the number of ways to form such teams, is. . . .

The number of matrices of order $3 \times 3$, whose entries are either $0$ or $1$ and the sum of all the entries is a prime number, is$....$