How many ways can 6 boys and 4 girls stand in a row if the girls must not be together?
Arrange all 6 boys in a row . --> ways to do this is 6!
This leaves 7 gap in between the boys to place 4 girls in. -> $_7C_4$
The girls in between the boys can have 4! ways to arrange them.
therefore, answer is $6! \cdot _7C_4 \cdot 4! $
why am i wrong ?
the right answer is $6! \cdot _7C_4 \cdot 4! + 6! \cdot _7C_2 \cdot 4! + 6! \cdot _7C_2 \cdot 4!$