If there are 5 boys and 7girls, in how many ways can 5 boys and 5girls sit in a round table?

Is the ans : 5!*4!*7c5?

Reason: since there are 5 boys so (5-1)!
And left 5 seats for girls so 7c5 and within the girls theres 5 diffrent ones so another 5!

I forgot to add that the boys and girls need to be in alternated seats

To find the number of ways the 5 boys and 5 girls can sit in a round table, we need to consider two factors: the arrangement of the boys and the arrangement of the girls.

First, let's consider the boys. We have 5 boys, so the number of ways they can be arranged in a round table is (5-1)! = 4!. This is because in a round table, the arrangement is considered unique only when the positions of the people are unique relative to each other, not to the table itself.

Next, let's consider the girls. We have 7 girls, but only 5 seats available for them. Therefore, we need to choose 5 girls out of 7 to occupy those 5 seats. The number of ways to choose 5 girls out of 7 is denoted as 7C5.

Finally, within the group of 5 girls, they need to be arranged among themselves. So there are 5! ways to arrange them.

To find the total number of ways, we multiply the number of ways to arrange the boys, the number of ways to choose the girls, and the number of ways to arrange the girls:
Total number of ways = 4! * 7C5 * 5!

So, the answer is not just 5!*4!*7C5, but rather 4! * 7C5 * 5!.