The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by

Question

Smart Achievers · Accepted Answer

(4)

Number of women = 5

Number of men = 6

Number of ways of arranging 6 men at a round table is $(n - 1)!$

= $(6 - 1)!$

= $5!$

Now we are left with six places between the men, and there are 5 women. These 5 women can be arranged in these places in ${}^{6}P_{5}$ ways.

$∴$ The required number of ways

= $5! \times {}^{6}P_{5}$

= $5! \times 6!$

Want Us to Email you About Special Offers & Updates?