In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate.

when seating 4 boys and 3 girls alternatively in a row, consider them as distinct entities. you have 7 individuals to arrange.
the possible arrangements for B (boys) and G (girls) are as follows:

1. BGBGBGB
2. GBGBGBB
3. GBGBBGB
there are 2 possible arrangement for the sequence of B and G. within each gender, the individuals can be arranged among themselves.

so, the total number of ways is (2times 4!time 3!=2times 24 times 6 = 288).

therefore, there are 288 ways to seat 4 boys and 3 girls alternatively in a row.

Dear Nagamani,
! means "Factorial"
Ex: 1!=1
2!=1x2=2
3!=1x2x3=6
4!=1x2x3x4=24
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n!=1x2x3x4x5x6x........xn

Thanks..

i dont understand these solutions what 4!3!means what '!' symbolises