C(n + r – 1, r)

to find out that with n = 4 color possibilities and r = 2 colors per packet, there are:

C(4 + 2 – 1, 2) = C(5, 2) = 5! / (2! * (5 – 1)!) = 10

possible combinations of colors you can receive.

Now assuming (by educated guess), the popularity of Starburst flavors in order from least to most popular is yellow, orange, pink, red, we can list out these 10 poker hands in order from worst to best:

The “high card” hands:
Yellow, Orange
Yellow, Pink
Yellow, Red
Orange, Pink
Orange, Red
Pink, Red
and the “pair” hands:
Yellow, Yellow
Orange, Orange
Pink, Pink
Red, Red

So assuming a uniform distribution, there is a 10% chance of getting any of the above hands. That also means a 40% chance of getting a pair of colors, a 40% chance of getting at least one yellow, and a 40% chance of getting at least one red.

Happy playing.

I find it interesting that businesses decided it was best practice to speak in broad, ambiguous, extra cheesy, extra cheery, overenthusiastic, broadcast-mode-only, politically correct, extra-safe PR-speak in the first place. My guess is customers never suggested, requested, or desired that businesses go so far down the PR-speak rabbit hole that they would become a parody of themselves.

I find it interesting that even with the rise of the Internet, discussion forums, chat rooms, blogging, MySpace, Second Life, and (pre-Twitter) Facebook, where on relatively rare occasions businesses would respond to individual people, the phoniness continued. And I find it extremely interesting that it took Twitter to be popularized for businesses to start considering conversing with their customers in a genuinely human sort of way.

And even more interesting is that many hire “social media experts” to teach them how to talk like a human being.

So we’ve come full circle: people who founded brands sort of gave up their humanity so they could market like a conventional business and now they’re looking to go back to acting like the humans they are — except they’re clumsy and fumbling or just don’t remember how.

I like to meet new people from many different backgrounds and so I often find myself in the company of marketing types who don’t get/like social media. Though it’s easy to dismiss these kinds of people as putting their heads in the sand because they irrationally can’t accept change and you just want to say “stop whining and deal with it; evolve or die” I recently came to a realization: there’s another aspect to this. It’s not just that some people don’t know how to be transparent and genuine and human and it’s not just that they’re in denial about where the eyeballs are or the habits and behaviors of certain large chunks of the population (in my experience this is a “well I don’t like/do this so the majority of people don’t like/do it either” mindset).

There’s another fundamental reason as to why traditional media marketers are having trouble. These people are used to TV and radio commercials, newspaper and banner ads, billboards and flyers. What all of these things have in common is you create it one time, put it out there, and move on to the next thing. I call it set-it-and-forget-it marketing.

But with new media (and even with web 1.0 websites), the media and effort is all organic and it needs to evolve and be maintained over time, pivoting and tweaking based on gathered measurements, responses, new data, and experimentation. This is a long-term proposition, not a shotgun blast. It’s more work and the payoff isn’t immediate. I think this is what is hard for people to accept.

It’s a big, global cocktail party out there. You wouldn’t go to a cocktail party screaming about savings and blasting a volume-inappropriate jingle like a used car salesperson on the radio.

My guide to social media:
1. Do awesome work.
2. Be yourself.
3. Have conversations.

That’s it.

A = 100%, B = 0%, C = 0%
A = 99%, B = 1%, C = 0%
A = 99%, B = 0%, C = 1%
A = 98%, B = 2%, C = 0%
A = 98%, B = 1%, C = 1%
A = 98%, B = 0%, C = 2%

…and so on.

I spent a few minutes toying with different approaches, but nothing obvious jumped out.  Then I realized that in cases like this, it helps to rephrase the problem into something simpler, an equivalent problem that can be more easily modeled (or attacked algorithmically).  I took the perspective that what we’re really trying to do here is distribute 100 percentage points amongst a collection of ingredients standing in a line.  The first ingredient takes some amount of percentage points from the proverbial bucket, then passes the bucket to the next ingredient; the last ingredient in the line is stuck with the remaining percentage points passed to it (i.e. the entire contents of the bucket).  Some ingredient will take all 100 some of the time, leaving none for any other and that’s ok; other times, an ingredient will take 0 percentage points when it could take a lot more and that’s ok too.

After I approached the problem with this 100-points-in-a-bucket-passed-down-a-line model, the code started to flow.  And this is what I gave to my friend (in PHP):

    function distribute($distribution_array, $current_index, $rest_count)
    {
        // if the current ingredient is at the last one in the line...
        if($current_index == count($distribution_array) - 1)
        {
            // take the rest
            $distribution_array[$current_index] = $rest_count;

            // print the array's contents
            print_r($distribution_array);
            echo '<br/>';
        }
        else
        {
            // for every possible amount of percentage points I am able to take...
            for($take_count = $rest_count; $take_count >= 0; $take_count--)
            {
                // take the amount of percentage points
                $distribution_array[$current_index] = $take_count;

                // and distribute the remaining down the line
                distribute($distribution_array, $current_index + 1, $rest_count - $take_count);
            }
        }
    }

    // distribute to a line of 3 ingredients, starting at the first ingredient, 100 percentage points
    distribute(array(0, 0, 0), 0, 100);

Of course the number of combinations grows exponentially as the number of ingredients increases. That, taken with the facts that even three ingredients produces far more combinations than anyone should actually try and that a one percent difference in any given ingredient probably won’t affect the end result much, I suggested to my friend to look at varying the proportions by intervals of ten or twenty percent rather than one percent (i.e. change “$take_count–” on line 15 to “$take_count -= 10″).

Of course there are always exceptions.  Some designers do actually write clean, maintainable pages that work in all popular browsers; and some even enjoy doing it.  I think that’s great and I’m *always* for generalism, but I worry when I see job ads looking to hire web designers that require knowledge of HTML, CSS, and sometimes even Javascript and PHP/ASP/etc!  Unless I’m totally underestimating the number people out there who can design well *and* code well, it’s pretty insane.

Sometimes you just have to let the designers design and the developers develop. If that’s the case then the designers who just want to design are happy and certain developers are happy — the kind who don’t mind the grunt work resulting from a stream of unchallenging “Make a web page that looks like this Photoshop document.” requests.

Now I’m not trying to put down designers because what they do is extremely impressive, valuable, and something I could never do (it’s just not in *my* DNA).  Naturally everything about this  works both ways: developers don’t tend to be great designers and if you were to ask me to design a webpage, you would probably get something decidedly uninspired, unappealing, and unartistic.  But you don’t see job postings for developers requiring InDesign experience.