JEE MainMathematicsPermutation and Combination
If all the words, with or without meaning, made using all the letters of the word "SECRET" are arranged as in a dictionary, then the rank of the word "SECRET" is :
Options
- A253
- B254
- C255
- D393
Correct answer
C. 255
Step-by-step solution
The letters of the word "SECRET" in alphabetical order are C, E, E, R, S, T. Number of words starting with C = 5! 2! = 60 Number of words starting with E = 5! = 120 Number of words starting with R = 5! 2! = 60 Sum of words starting with C, E, and R = 60 + 120 + 60 = 240 The next words start with S. We need the word SECRET, so we look at the second letter. Number of words starting with SC = 4! 2! = 12 Sum of words so far = 240 + 12 = 252 The next words start with SE. The available letters are C, E, R, T. Number of w