Answer
24
Work Step by Step
The Fundamental Counting Principle$:$
The number of ways in which a series of successive things can occur is found by multiplying the number of ways in which each thing can occur.
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The 5th perfomance is "reserved" for the singer that requested so.
Once a performer is chosen, there is one less left to choose from.
So,
1. The 1st singer can be chosen in $4$ ways.
2. The 2nd singer can be chosen in $3$ ways.
3. The 3rd singer can be chosen in $2$ ways.
4. The 4th singer can be chosen in $1$ ways.
5. The 5th singer can be chosen in $1$ ways.
Total ways to arrange the performances:
$4\times 3\times 2\times 1\times 1=4!=24$