Find the number of ways seven boys and three girls can be seated in a row if the girls sit together at one end of the row

combinatoricspermutations

Find the number of ways seven boys and three girls can be seated in a
row if the girls sit together at one end of the row.

I'm struggling with the 'end of the row' part of the question.

Best Answer

Take two cases, one where all the girls sit on the left hand side, and one where they all sit on the right hand side.

For the girls sitting on the LHS you'll get $G_1G_2G_3B_1B_2...B_7$ which will have $3!7!$ number of combinations.

Then you'll get the same amount of combinations with the girls all sitting on the RHS.

So then your answer should be $2\times3!7!$