${ }^{n+2} P_{r+2}$

${ }^{n+2} P_{r+1}$

$(n+1)$ !

${ }^{n+1} P_{r+1}$

the number of ways in which $n$ boys and $n$ girls can be arranged in a row.

the number of ways in which $n$ boys and $n$ girls can be arranged in a row such that all the girls are together.

the number of ways in which $n$ boys and $n$ girls can be arranged in a row such that no two girls are together.

the number of ways in which $n$ boys and $n$ girls can be arranged in a row such that no two girls are together and no two boys are together.

75

57

51

33