Find the number of possible arrangements of the letters in the word PENCILS if 'E' comes before 'I' ?

1 Answer
Apr 30, 2018

#(7!)/2 = 2520#


In any arrangement of the word ‘PENCILS’, there will (obviously be 1 ‘e’ and 1 ‘i’. In every arrangement , either e comes before i or after. Also, for every arrangement where i comes before e , we can switch the places of e and I so that e comes before i. Therefore the total number of permutations (arrangements) where e comes before i is total arrangements divided by 2 #=(7!)/2 = 2520 #