Question

Assertion :The no.of circular permutations of $7$ persons taken $4$ at a time is $\frac{{}^7{P}_4}{4}$ Reason: The no.of circular permutations of $n$ different things taken $r$ at a time is $\frac{{}^n{P}_r}{r}$

• A. Assertion is correct and Reason is incorrect
• B. Assertion is incorrect and Reason is correct
• C. Both Assertion and Reason are correct
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is C Both Assertion and Reason are correct

The number of circular permutations of $r$ things is $(r-1)!$
The number of ways we can select $r$ things from $n$ things is ${}^n{C}_r$
The number of ways of selecting r people and arranging them around a circle is ${}^n{C}_r\times (r-1)!=\frac{n!}{r!(n-r)!}\times (r-1)!=\frac{{}^n{P}_r}{r}$
Hence, both Assertion and Reason are correct.