In how many ways can 18 girls and 15 boys sit in a row such that just the girls are always next to each other?

combinatorics

In how many ways can 18 girls and 15 boys sit in a row such that just the girls are always next to each other?

Now I have 2 * 18! x 15!

But I am not sure with this.


Solution 1:

If just the girls can sit togeher , then all of the boys must be separate from one another. Then arrange the girls by $18!$ ways in the row , this arrangement gives $19$ possible places for boys including end points and gaps between girls .You can place the boys by $P(19,15)$ or $C(19,15)15!$. Then , $$18! \times P(19,15)$$

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