Question

There are

6

acts in a talent show.

A comedian, a dancer, a juggler, a magician, a pianist, and a singer.

A talent show host randomly schedules the

6

acts.

Compute the probability of each of the following events.

Event A: The pianist is first, the juggler is second, the singer is third, and the comedian is fourth.

Event B: The first four acts are the dancer, the juggler, the magician, and the comedian, in any order.

Answer 1

Number of ways they can perform=6!=720

Number of ways the pianist is first, the juggler is second, the singer is third, and the comedian is fourth=2!=2

Probability that the pianist is first, the juggler is second, the singer is third, and the comedian is fourth==

Number of ways the   first four acts are the dancer, the juggler, the magician, and the comedian, in any order=4!2!=24*2=48

Probability that the first four acts are the dancer, the juggler, the magician, and the comedian, in any order==.