Question

In how many ways can you seat 5 women and 5 men in a row if women must seat next to each other,men must seat next to each other, and 2 women are indistinguishable siamese twins (also dressed alike)?

Answer 1

Answer: 288ways

Step-by-step explanation:

There are 5men and 5women to be arranged, since the men must seat together, they will be arranged in 5! ways. For the women, since they must also seat together but with siamese twins between them, they can be arranged in 4! ways instead of 5! ways and this is due to presence of the twins among them.

Note that Siamese twins cannot be separated as such both are taken as one making it 4!.

Since the women and men are always sitting together, they can be arranged in 2! ways i.e 2 sexes

The final seating arrangement can be done in 2!×(5!+4!) ways

= 2× (120+24)

= 2×144

= 288ways.

Note that the arrangement of the men and women are added because they can only be arranged differently to ensure different sex are not sitting together.