Answer
The number of ways to arrange the program at a concert is\[541,900,800\].
Work Step by Step
The first performance is done by jazz group, then the performance can happen in 8, for the second performance there is 8 ways as rock band is performing. For the third performance, there are 7 possibilities for occurring of the jazz as one performance of jazz group is already performed.
For a 4thto 7th position, the performance of rock band can be computed in\[_{7}{{C}_{4}}\]ways, for 8th place, there are 6 possibilities as two jazz performance were done before. For the remaining 8 places, the performance can be arranged in\[8!\].
Compute the number of ways to arrange the program at a concert using the equation as shown below:
\[\begin{align}
& \text{number of ways to arrange the concert}=8\times 8{{\times }_{7}}{{C}_{4}}\times 6\times 8! \\
& =8\times 8\times 7\times \frac{7!}{4!\left( 7-4 \right)!}\times 6\times 8! \\
& =2688\times \frac{7!}{4!3!}\times 40,320 \\
& =3,793,305,600
\end{align}\]
Hence, the number of ways to arrange the program at a concert is\[541,900,800\].
