Question

Suppose that there are m girls and n boys in a class. What is the number of ways of arranging the students in a line so that Arman and Aisha (boy and girl) never stand together? Explain?

Answer 1

count the number of ways to arrange the m+n kids.

then subtract the number of ways that Arman and Aisha cound be put together

Answer 2

Suppose Arman and Aisha are always put together. Then, considering them as one entity, we have a total of m + n - 1 people. These people can be arranged in 2(m + n - 1)! different ways.

Now total number of ways in which m + n people can be arranged are (m + n)!. Hence number of ways in which Arman and Aisha are not put together are (m + n)! - 2(m + n - 1)!

Answer 3

Thank you very much.

Answer 4

Your welcome.