Just an extension of the problem. In how many ways can one post 5 letters in 10 different letter boxes if no more than one letter should be posted in the same letter box?
think this way. You have 10 choices for the first letter, then 9 choices for the second letter, the 8 choices for the third letter.
Hence, you have 10*9*8*7*6 = 30240.
This can also be thought of as an "arrangement" or "permutation" problem.
How many ways can you assign a mailbox number to 5 different letters without repeating from a choice of 10 numbers. 10P5 = 10!/5! = same solution as above.
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