Answer to Question #101219 in Statistics and Probability for Angelica nero

Question

In how many ways can 3 boys and 2 girls sit in a row if the boys and girls are each to sit together?

Answer 1

Number of boys = 3

Number of girls = 2

Now we need to arrange in such a way that boys will sit together and girls will also sit together. So, we need to consider all boys as 1 and all girls as 1.

So number of ways to keep boys and girls together = ²P₂ = 2

But boys can also be arranged among them and girls can also be arranged among them.

So total number of arrangements in which boys will be together and girls will be together

= ²P₂ * ³P₃ * ²P₂

= 2 * 6 * 2

= 24 ways