4 boys and 5 girls are to form a line. Find the number of permutations in which no two girls stand next to each other

Sure, here is the step by step solution:

Step 1: Arrange the boys first. There are 4 boys, so the number of ways to arrange them is 4! = 432*1 = 24 ways.

Step 2: There are 5 spaces between and on the sides of the boys where the girls can stand to ensure that no two girls are next to each other ( B_B_B_B ). So we need to place 5 girls in these 5 spaces. The number of ways to do this is 5P5 = 5! = 54321 = 120 ways.

Step 3: Multiply the number of ways from step 1 and step 2 to get the total number of permutations. So, 24*120 = 2880.

Therefore, there are 2880 ways to arrange 4 boys and 5 girls in a line such that no two girls stand next to each other.