Question 2: In how many ways can 4 boys and 4 girls be seated around a circular table so that no two boys are in adjacent positions?

To solve this problem, we can use the concept of permutations and combinations.

Step 1: Arrange the 4 girls around the circular table. The number of ways to do this is (4-1)! = 3! = 6 ways. We subtract 1 because in circular permutations, the number of arrangements is (n-1)!.

Step 2: Now, we have 5 spots left for the boys (4 spots between the girls and 1 spot after the last girl which is actually the first spot before the first girl due to the circular arrangement).

Step 3: We can arrange the 4 boys in these 5 spots in 5P4 ways. The formula for permutations is nPr = n! / (n-r)!. So, 5P4 = 5! / (5-4)! = 5! / 1! = 120 ways.

Step 4: Multiply the number of ways from step 1 and step 3 to get the total number of arrangements. So, 6 * 120 = 720 ways.

So, there are 720 ways to arrange 4 boys and 4 girls around a circular table so that no two boys are in adjacent positions.