Permutation and Combinations with conditions Hallo :) This is a question about permutations but with conditions.
2 boys and 4 girls are to be arranged in a straight line.
In how many ways can this be done if the two boys must be separated? (The order matters)
Thank You.

Total number of ways of arranging the people = 6!
Cases when boys are together:
(2B) G G G G
G (2B) G G G
G G (2B) G G
G G G (2B) G
G G G G (2B)
Each of the above combinations can be arranged in 2 * 4! ways.
(The factor of 2 is accommodated since the boys themselves could be interchanged, as they are on a straight line.)
Number of ways to separate the boys = (6! - (2 * 5 * 4!)) = 5! * (6 - 2) = 480
