Q55 / 160 · AP EAMCET 2024 (22 May Shift 2) · Mathematics

The number of ways of arranging 9 men and 5 women around a circular table so that no two women come together are

A
$8!^8 P_5$
B
$9!{ }^9 P_5$
Correct answer
C
$8!{ }^9 P_5$
D
$8!5$ !

Solution

First fix the men in circular arrangement, which can be done in $(9-1)!=8$ ! ways Now, there are 9 places between the men and 5 womens to be seated between the men. That can be done in ${ }^9 \mathrm{P}_5$ ways. $\therefore$ Total no. of ways to sit $=8!{ }^9 \mathrm{P}_5$

Hence, the correct answer is option: 'C'.

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