We are running partition once on an array of $5$ unique elements.

$($a$)$ How many possible arrangements of the original array values are there so that partition will split the array into $2$ elements on the left and $2$ elements on the right $($the pivot ending up exactly in the middle of the array$).$ Arrangement examples: If the array is made up of the elements $10,20,30,40,50,$ possible arrangements include $[10,20,50,40,30],[10,50,20,40,30],...$

$($b$)$ Explain your answer to $($a$).$

Solution:

$[5$ pts$]$

$[5$ pts$]$

Number of Possible Arrangements