Question

Ten guests are to be seated in a row of which three are ladies. The ladies insist on sitting together while two gentlemen refuse to take consecutive seats. In how many ways can the guest be seated?

• A. $2399976$
• B. $21844$
• C. $630624$
• D. $181440$

Answer 1

The correct option is A $2399976$

If three ladies are together and two men are together $=7!\times 3!\times 2!$

If three ladies are together and no-condition of that particular two men $=8!\times 3!$

$\therefore$ The required answer $=8!\times 3!-7!\times 3!\times 2$

$\Rightarrow 7!\times 3!(8-2)$

$\Rightarrow 7!\times 3!\times 6$

$=181440$.