Consider a coding system where C, H, A, S, M = 2, 3, 1, 5, 4 respectively. We want to know the rank of code 23154.
Let's count all of the possible combinations below 23154.
We know that any code starting with 1 is less so we have 4! = 24 possibilities.
We also know that any cod starting with 21 is less so we have 3! or 6 additional possibilities.
For codes starting with 23XXX, only 23145 is less than 23154. so we have a total of 31 codes less than 23154 so the rank of cod 23154 is 32 and the answer, IMO, is (3).
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993