Problem 3 of 3

At a concert, the program included three vocal presentation and two piano presentations.

(a) In how many ways can the program be arranged so that it includes all the presentations?

(b) In how many ways can the program be arranged if piano and vocal presentations alternate?

(c) If the order of the presenations was randomly selected, what is the probability that piano and vocal presentations would alternate?

(d) You are giving one of the piano presenations. If the order of the presentations is randomly arranged, what is the probability that you will go first?

Solution