Question

In how many ways can 6 gentlemen and 4 ladies be seated round a table so that no two ladies are together.

Answer 1

There are 6 vacant places in between the 6 gentlemen and 4 ladies can occupy these gaps in ⁶P₄ ways. 

For each of these the six gentlemen can be permuted in (6 – 1)! = 5! 

∴ The number of ways is 5!⁶P₄