Combo Problem

[phaelan.vaillancourt]

This question is from ETS practice test that I have attempted my approach however it is incorrect:

A certain ID code is list of five symbols: SSDDD. Each of first two symbles much be one of 26 letters of English alphabet and each of the last 3 symbols must be one of the 10 digits. Repeated letters and digits not allowed. What are the total number of digits?

A) 1,757,600
B) 676,000
C) 468,000
D) 1,676
E) 82


My attempted solution (incorrect):

26*26= 676 - 26 (total repeat leters, i.e. AA, BB...ZZ) = 650
total combo of numbers 10*10*10 - 10*9 (repeat digits - 112,113,..991,etc) -10*9 (repeat digits 011,211, etc.) -10*9 (101, 121...919, etc) = 730

650*730 = 474,500 BUT this is incorrect. Some help? THANK YOU!


The above 10*9 means I am deleteing the repeated digit values (112,113,..991,etc

[tommywallach]

Hey Phaelan,

Definitely don't do subtraction like this on combinatorics. It's much easier to just define each slot by the number of options for that slot:

26 * 25 * 10 * 9 * 8 = 468,000

Voila!

-t