The number of distinguishable arrangements of the letters of the word S E X D E C I L L I O N

Answer 1

There are 12 letters, including 2xE, 2xI, 2 x L

12! / (2! 2! 2!) =

12*11*10*9*8*7*6*5*4*3*2 / (2*2*2) =

12*11*10*9*8*7*6*5*4*3 / (2*2) <-- 2 cancels

12*11*10*9*8*7*3*5*2*3 <-- 6 and 4 cancels the 2's

59,875,200