A computer file can be given a name consisting of at least 6 but no more than 8 chracters. characters that can be used are: all letters of the English alphabet *not case sensitive* and digits (0 to 9). The computer file name must contain at least one letter and one digit. How many different possible names are there?
*the solution may require several different cases, each adding up to the final answer. (i don't know what the answer is) *with permutations, order matters
My work so far: 26 letters + 10 digits = 36 characters in total
Case 1 26 x 10 x 10 x 10 x 10 x 10 = 2,600,000
i only did one case but is this even correct? the total seems rather large.
You are correct in stating that you must consider cases, i.e. file names of either 6, 7, or 8 characters.
Let us look at the case where the length is 6. You can follow the same pattern for 7 and 8.
The easiest way to solve this is to consider the total number of possibilities and subtract from that the cases where there are no letters and the cases where there are no digits.
Total number of permutations: 36^6. Cases where there are no digits: 26^6 (all letters) Cases where there are no letters: 10^6 (all digits)
Therefore the total number that contain at least one letter and one digit are 36^6-26^6-10^6.
permutations
Posted - 10/31/2009 : 12:34:46
