#2**+10 **

Mekody.....I think this questioner wants to know how many different "PIN" numbers can be created by using "FACTORIALS." (not, Victorials !!!)

Of course, we would have to know the specifics, but here's a simple example:

Suppose we hade a 6 character "PIN" number consisting of 3 letters and 3 digits, and we allowed repeats. So the total number of possible "PINs" could be formed thusly:

Choose any 3 "slots" to put the letters in, and in each of these slots, we would have 26 choices for the selection of a letter. And for each of these arrangements, we would have 100 possible digit combinations to fill the other 3 "slots" (000-999).

So the total number of "PINs" is just

C(6,3)*26^{3} *100 = [6! / (6 - 3)! * 3!] * 26^{3} * 100 = 35,152,000 possible "PINs"

[I think this is correct !!!]

CPhill
Oct 14, 2014

#2**+10 **

Best Answer

Mekody.....I think this questioner wants to know how many different "PIN" numbers can be created by using "FACTORIALS." (not, Victorials !!!)

Of course, we would have to know the specifics, but here's a simple example:

Suppose we hade a 6 character "PIN" number consisting of 3 letters and 3 digits, and we allowed repeats. So the total number of possible "PINs" could be formed thusly:

Choose any 3 "slots" to put the letters in, and in each of these slots, we would have 26 choices for the selection of a letter. And for each of these arrangements, we would have 100 possible digit combinations to fill the other 3 "slots" (000-999).

So the total number of "PINs" is just

C(6,3)*26^{3} *100 = [6! / (6 - 3)! * 3!] * 26^{3} * 100 = 35,152,000 possible "PINs"

[I think this is correct !!!]

CPhill
Oct 14, 2014