The letters of the word 'SUCCESS' are written in all possible orders and arranged in a serial order as in an English dictionary. If the 300^ th word in this arrangement is found, and its vowels are located at the i^ th and j^ th positions (counting from the left, starting with 1 ), then the value of i^2 + j^2 is

Step-by-step solution

The letters of the word SUCCESS in alphabetical order are C, C, E, S, S, S, U. First, we find the number of words starting with each letter: Words starting with C: 6! 3! = 120 Words starting with E: 6! 3!2! = 60 Total words so far = 120 + 60 = 180 . Words starting with S: 6! 2!2! = 180 . The 300^ th word lies in the block of words starting with S. We need the (300 - 180) = 120^ th word starting with S. For words starting with S, the remaining letters are C, C, E, S, S, U. Words starting with SC: 5! 2! = 60 Words st