How many arrangements of the letters a b c d leave none of t

How many arrangements of the letters a, b, c, d leave none of the letters a, b or c in their original positions

Solution

Total number of arrangement = total arrangement of all four letters - # of arrangement where a is remain at its original position - # of arrangement where b is remain at its original position - # of arrangement where c is remain at its original position # of arrangement where d is remain at its original position

= 4! - 3! -3! 3! = 4! - 3x 3!

= 24 - 18 = 6