Question

There are n seats round a table numbered $1,2,3,...,n$. The number of ways in which $m(\le n)$ persons can take seats is

• A. ${}^n{P}_m$
• B. ${}^n{C}_m\times (m-1)!$
• C. ${}^{n-1}{P}_{m-1}$
• D. ${}^n{C}_m\times m!$

Answer 1

Answer: (A), (D)

The correct options are
A ${}^n{P}_m$
D ${}^n{C}_m\times m!$

Since $M\le N$ and there are no restrictions, then

The number of ways will be

$={}^n{P}_m$

$=\frac{n!}{(n-m)!}$

$=\frac{n!\times m!}{(n-m)!.m!}$

$={}^n{C}_{m}m!$

Hence answers are $A$ and $D$.