# In how many ways can 5 boys and 2girls be arranged ata table if 2 girls are never together?

In how many ways can 5 boys and 2girls be arranged ata table if 2 girls are never together?

## Answer/Solution

480

### Steps/Work

Total ways of arranging 7 person in a circle = 6! = 720 ways

If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways

And two women can arrange themselves in 2! ways

Total ways in which two women sit together in circle = 5!*2! = 240 ways

Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways

E

If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways

And two women can arrange themselves in 2! ways

Total ways in which two women sit together in circle = 5!*2! = 240 ways

Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways

E