$2$ Eigenfunction Decomposition of Wavefunctions

$($A$)(5$ points$)$ For the $1$D particle$-$in$-$a$-$box wavefunction $($boundaries at $x=0$ and $x=4)$ defined

by $(x)=\sqrt[\phantom{2}]{\frac{1849845}{20278151217152}}(x-3{)}^3{x}^2(x-4{)}^5$ calculate the five three energy states that would be

observed in any given experiment, as well as their probability of observation.