Find the number of ways in which 5 boys and 5 girls can be seated in a row so that(a) No two girls may sit together

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

Step 1: Arrange the boys first. There are 5 boys, so they can be arranged in 5! (factorial) ways, which is 54321 = 120 ways.

Step 2: Now, we need to arrange the girls in such a way that no two girls are sitting together. To do this, we can think of the boys as creating 6 "spaces" where the girls can sit (one on either side of each boy, and one at each end of the row). So, we need to place 5 girls in these 6 spaces. This can be done in 6P5 ways (permutations of 6 things taken 5 at a time), which is 65432 = 720 ways.

Step 3: Multiply the number of ways from step 1 and step 2 to get the total number of ways the boys and girls can be seated. So, 120 * 720 = 86,400 ways.

So, there are 86,400 ways in which 5 boys and 5 girls can be seated in a row so that no two girls may sit together.