How to find total possible values from length and characters?

Question

I'm totally not a Math whiz kid here, but have put together a function with the great help of StackOverflow (and a lot of trial and error) that generates a random serial number from a Formula, group of Letters/Numbers, and array (so as to not duplicate values).

So, my current formula is as follows:

$.extend({
    generateSerial: function(formula, chrs, checks) {
        var formula = formula && formula != "" ? formula : 'XXX-XXX-XXX-XXX-XXX', // Default Formula to use, should change to what's most commonly used!
            chrs = chrs && chrs != "" ? chrs : "ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789",  // Default characters to randomize, if not defined!
            len = (formula.match(/X/g) || []).length,
            indices = [],
            rand;

        // Get all "-" char indexes
        for(var i=0; i < formula.length; i++) {
            if (formula[i] === "-") indices.push(i);
        }

        do {
            rand = Array(len).join().split(',').map(function() {
                return chrs.charAt(Math.floor(Math.random() * chrs.length));
            }).join('');

            // Rebuild string!
            if (indices && indices.length > 0)
            {
                for(var x=0; x < indices.length; x++)
                    rand = rand.insert(indices[x], '-');
            }
        } while (checks && $.inArray(rand, checks) !== -1);

        return rand;
    }
});

Ok, so, what I need to be able to do is to find total possible values and make sure that it is possible to generate a unique serial number before actually doing so.

For example:

var num = $.generateSerial('XX', 'AB', new Array('AB', 'BA', 'AA', 'BB'));

This will cause the code to do an infinite loop, since there are no more possibilties here, other than the ones being excluded from the extension. So this will cause browser to crash. What I need to be able to do here is to be able to get the number of possible unique values here and if it is greater than 0, continue, otherwise, don't continue, maybe an alert for an error would be fine.

Also, keep in mind, could also do this in a loop so as to not repeat serials already generated:

var currSerials = [];
for (var x = 0; x < 5; x++)
{
     var output = $.generateSerial('XXX-XXX-XXX', '0123456789', currSerials);
     currSerials.push(output);
}

But the important thing here, is how to get total possible unique values from within the generateSerial function itself? We have the length, characters, and exclusions array also in here (checks). This would seem more like a math question, and I'm not expert in Math. Could use some help here.

Thanks guys :)

Here is a jsFiddle of it working nicely because there are more possible choices than 16: http://jsfiddle.net/qpw66bwb/1/

And here is a jsFiddle of the problem I am facing: Just click the "Generate Serials" button to see the problem (it continuously loops, never finishes), it wants to create 16 serials, but 16 possible choices are not even possible with 2 characters and only using A and B characters: http://jsfiddle.net/qpw66bwb/2/

I need to catch the loop here and exit out of it, if it is not able to generate a random number somehow. But how?

Answer 1

The number of possible serials is len * chrs.length, assuming all the characters in chrs are different. The serial contains len characters to fill in randomly, and chrs.length is the number of possible characters in each position of that.