Question

Five persons are to address a meeting. If a specified speaker is to speak before another specified speaker, find the number of ways in which this could be arranged. In how many of these arrangements will the first speaker come immediately before the second?

Answer 1

Let A, B be the corresponding specified speakers.

(a) Without any restriction the five persons can be arranged among themselves in 5! ways; but the number of ways in which A speaks before B and the number of ways in which B speaks before A together make up 5!. Also, the number of ways in which A speaks before B is exactly equal to the number of ways in which B speaks before A.

Therefore, the required number of ways = 1/2.5! = 60.

(b) Regarding AB in that order as a single person, we can arrange them with the remaining three in 4 ways. Each of these arrangements corresponds to a way in which A speaks immediately before B.

Therefore, the required number of ways in this case = 4! = 24.