#color(blue)("Consider "color(white)()^6P_4)#
#(n!)/((n-r)!)->(6!)/((6-4)!) =(6xx5xx4xx3xx2xx1)/(2xx1)#
Really the #xx1# is not needed but I included it for completeness.
#=(6xx5xx4xx3xxcancel(2xx1))/(cancel(2xx1)) = 360#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider "color(white)()^8C_3)#
#(n!)/((n-r)!r!) ->(8!)/((8-3)!3!)#
#(8xx7xx6xx5!)/(5!xx3xx2)#
#(cancel(8)^4xx7xxcancel(6)^2xxcancel(5!))/(cancel(5!)xxcancel(3)^1xxcancel(2)^1) = 56#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#
#360+56 = 416#
