Notations of Permutations

Q. What is the value of $\text{n.P(n-1, r-1)}$?

1. $\text{P(n, r)}$
2. $\text{P(n, n)}$
3. $\text{P(r, r)}$

Q. $\frac{3!}{0!}$ can also be written as which of the following?

1. ${}^3{P}_0$
2. ${}^3{P}_3$
3. ${}^0{P}_3$
4. Can't be determined

Q. What is the value of ${}^m{P}_{m-1}$?

1. $\frac{m!}{m!}$
2. $\frac{m!}{(m-1)!}$
3. $m!$
4. None of the above

Q. If ${}^{10}{P}_r=5040,$ Then what is the value of $r.$

1. $r=6$
2. $r=10$
3. $r=4$
4. $r=8$

Q. What is the correct notation of permutation of $n$ different things taken $r$ at a time with or without repetition?

1. ${}^n{P}_r$
2. $P_r^n$
3. $\text{P(n, r)}$
4. ${}_r^{n}P$