The number of permutations of n different things taken more than 'r' at a time when each thing may be repeated is

\frac{n (n^{r} - 1)}{n - 1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{n (n^{n} - n^{r})}{n - 1}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

^{n} P_{r} +^{n} P_{r}_{+}_{1} + . . . . . . +^{n} P_{n}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{n (n - r)}{n - 1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{n (n^{n} - n^{r})}{n - 1}$
Permutation of $r + 1$ objects $\to n^{r + 1}$
$r + 2$ objects $\to n^{r + 2}$
..........
..........
$n$ objects $\to n^{n}$
S $=$ $n^{r + 1} + n^{r + 2} + . . . . . . . . . . . . . . . . . . . . . . . + n^{n}$
S $=$ $\frac{n^{r + 1} (n^{n - r} - 1)}{n - 1}$
S $=$ $\frac{n (n^{n} - n^{r})}{n - 1}$

Suggest Corrections

Similar questions

n

r

List I	List II
A. The number of ways of answering one or more of $n$ questions	i. $\frac{^{n} P_{r}}{2 r}$
B. The number of ways of answering one or more of $n$ questions is when each question has an alternative is	ii. $2^{n} - 1$
C. The number of circular permutations of $n$ different things taken $r$ at a time is	iii. $\frac{^{n} P_{r}}{r}$
D. The number of circular permutations of $n$ things taken $r$ at a time none direction is	iv. $3^{n} - 1$
	v. $2^{n}$

The number of permutations of n different things taking r at a time when 3 particluar things are to be included is

Join BYJU'S Learning Program