Question

If P(n,n) denotes the number of permutations of different things taken all at a time then P(n,n) is not identical to:-

• A. $n.P(n-1,n-1)$
• B. $n.P(n,n-1)$
• C. $r!.P(n,n-r)$
• D. $(n-r)!.P(n,r)$

Answer 1

Answer: (B)

$n.P(n,n-1)$

$P(n,n)=\frac{n!}{(n-n)!}=n!$

Expanding every options

$n.P(n-1,n-1)$

$\Rightarrow n\cdot \frac{(n-1)!}{(n-1)!}=n!$

Identical

$n.P(n,n-1)$

$\Rightarrow n\cdot \frac{n!}{(n-(n-1\left)\right)!}=n.n!$

Not identical

$r!.P(n,n-r)$

$\Rightarrow r!.\frac{n!}{(n-(n-r\left)\right)!}=n!$

Identical

$(n-r).P(n,r)$

$\Rightarrow (n-r)!\frac{n!}{(n-r)!}=n!$

Identical