Question

Number of ways in which $n$ things of which $r$ alike and the rest different can be arranged in a circle distinguishing between clockwise and anticlockwise arrangement, is

• A. $\frac{(n+r-1)!}{r!}$
• B. $\frac{(n-1)!}{r}$
• C. $\frac{(n-1)!}{(r-1)!}$
• D. $\frac{(n-1)!}{r!}$

Answer 1

The correct option is B $\frac{(n-1)!}{r}$

Totally there are $n$ things out of which $r$ are alike.

We know that no. of ways of arranging $n$ thing in circular way $=(n-1)!,$ But $r$ things are alike, so similar to linear permutations.

Required $=\frac{(n-1)!}{r!}$

Hence, the answer is $\frac{(n-1)!}{r!}.$