# In how many ways can $6$ girls and $8$ boys be arranged in a row if no two girls should stand next to each other?

A teacher has 6 girls and 8 boys to arrange in for a choir. Determine the number of ways she can arrange the 14 children in a single row if no two girls should stand next to each other.

How do you do this? I just need to know how to solve this. You can use another example to explain this to me because this question is very tricky to me .

• Try 2 girls and 1 boy. Then 2 girls and 2 boys etc. to determine what the constraints are, and how many arrangements are possible satisfying the constraints. – Math Lover Sep 28 '17 at 22:25

$$\square b \square b \square b \square b \square b \square b \square b \square b \square$$ To separate the girls, choose six of these spaces in which to place the six girls.