Consider an object containing $9$ one$-$dimensional oscillators $($this object could represent a model of $3$ atoms in an Einstein solid$).$ There are $4$ quanta of vibrational energy in the object.

Part $1$

$($a$)$ How many microstates are there, all with the same energy?

$($b$)$ If you examined a collection of $50000$ objects of this kind, each containing $4$ quanta of energy, about how many of these objects would you expect to find in the microstate $000000004?$

Do NOT round to the nearest integer.