# If a class of 10 students has four men, how many ways can the men and women be arranged in a circle ...

If a class of 10 students has four men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?

## Answer/Solution

4!3!

### Steps/Work

for no two men to sit together, either all are in even or odd position

fix one at any one position then rest three can be fixed in 3! ways...

also rest four position of women can be fixed in 4!..

total ways 4!3!

C

fix one at any one position then rest three can be fixed in 3! ways...

also rest four position of women can be fixed in 4!..

total ways 4!3!

C