Question

The number of permutations of n dissimilar things taken not more than ‘r’ at a time, when each thing may occur any number of times is

• A. $\frac{n(n^r-1)}{n-1)}$
• B. $\frac{n(n^n-n^r)}{n-1)}$
• C. ${}^n{P}_1{+}^n{P}_2+\cdots \cdots {+}^n{P}_r$
• D. $\frac{n{(n-1)}^r}{n-1}$

Answer 1

The correct option is A $\frac{n(n^r-1)}{n-1)}$

$n+n^2+\cdots \cdots \cdots +n^r=\frac{n(n^r-1)}{n-1}$