Maybe something like this:
A2:A11 = 1,2,3,4,5,6,7,8,9,10
B2:B11 = checkboxes linked to the same cells as each checkbox is "in"
C2:C11: =RAND()
To get the random number try this array formula** :
=INDEX(A2:A11,MATCH(MAX(IF(B2:B11=FALSE,C2:C11)),C2:C11,0))
** array formulas need to be entered using the key combination of
CTRL,SHIFT,ENTER (not just ENTER)
Note that when you check/uncheck different checkboxes this will cause the
random number to change since RAND is a volatile function. You may want to
set calculation to manual and then hit F9 after you make your selections.