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Inverse of a Matrix

The number of...

Question

The number of circular permutations of $7$ dissimilar things taken $5$ at a time is

A

2520

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B

1260

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C

500

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D

504

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Solution

The correct option is C 504
Selection of $5$ things out of $7$ things can be done in $^{7} C_{5}$ ways and circular permutation of these $5$ things can be done in $(5 - 1)! = 4!$ ways.
Hence total number of required ways $=^{7} C_{5} .4! = \frac{7!}{5! .2!} \times 4! = 504$

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