3 girls and 3 boys can be seated at a circular table so that any two and only two of the ladies sit together. How many ways can they be seated?
My method was: 2 girls have to be seated toegther they can be arranged in 2! ways. You then have 1 girl and 3 boys left, 2 of the boys have to sit either side of the first 2 girls we placed as there cannot be 3 girls together. Those 2 boys can be places in 2! ways either side of the girls. There are then 2 places left where those places can be ordered in 2! ways. Giving 2x2x2=8 ways as the answer- which is way off the correct answer of 72, yet I cannot find an alternative way of thinking about it