In this question, n girls are to be seated alternatively between m boys.

There are m+1 spaces in which girls can be arranged.

The number of ways of arranging n girls is P(m+1,n) = ways.

Formula:

Number of permutations of n distinct objects among r different places, where repetition is not allowed, is

P(n,r) = n!/(n-r)!

Therefore, permutation of n different objects in m+1 places is

P(m+1,n) =

=

The arrangement of m boys can be done in P(m,m) ways.

Formula:

Number of permutations of n distinct objects among r different places, where repetition is not allowed, is

P(n,r) = n!/(n-r)!

Therefore, a permutation of m different objects in m places is

P(m,m) = = = m!

Therefore the total number of arrangements is .