color(blue)("Consider "color(white)()^6P_4)Consider 6P4
(n!)/((n-r)!)->(6!)/((6-4)!) =(6xx5xx4xx3xx2xx1)/(2xx1)n!(n−r)!→6!(6−4)!=6×5×4×3×2×12×1
Really the xx1×1 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
