A couple of misnomers

I'm still farting around with probabilities, even though I said I wouldn't for a while. The answer to how often a million heads in a row would show up are 1 in 2 to the millionth power. But how much is that in normal (base 10) numbers?

According to Web 2.0 Calc:

What is 2 to the millionth power?   

It is a very, very, very BIG NUMBER!!. It has 301,030 digits long!.If you were to print it on an ordinary paper, you would need about 150 pages of paper. It begins with: 9900656...........and so on.

That's a big number! I won't get into googols and googolplexes (as opposed to Google and the Googleplex), I'll save that for another math lesson.

Onto the misnomers:

Most people, me included, would call this device a combination lock, although the mathematically correct term would be permutation lock. A combination is a group of numbers where order doesn't matter, like the lotto where you pick 6 numbers out of 49 (or whatever number is decided upon). BTW - I just introduced you to the other misnomer but I'll get back to it.

In a "combination" lock, the order matters...5, 17, 12 is not the same as 17, 5, 12. The lock pictured above is mine, although I don't remember the "combination" to it...I'll try to figure it out later even though there are 64,000 different permutations (40 x 40 x 40). This would be considered a permutation with replacement because technically it's possible to repeat a number more than once. A lotto is similar but without replacement, which will bring us to our second misnomer.

Often a lotto game is called a Pick 6 (or Pick 5, or whatever). In math you use the term pick with permutations and choose with combinations. Pick and permutation both start with p, and choose and combination both start with c. So, the correct terminology would be Choose 6, not Pick 6. Above I said that a combination is where order doesn't matter...in a lotto, it doesn't matter what order the numbers are drawn, you just need to have the right numbers. I also said the lotto was without replacement. In the original California Lotto, it was a "Pick" 6 numbers out of 49. There were 49 ways to choose the 1st number, but only 48 ways to choose the 2nd, 47 ways to choose the 3rd and so on. Mathematically, it would look like this 49!/(43!6!), which means the odds of winning were 1 in 13,983,816. They've played around with it and it's currently "Pick" 5 out of 47 plus a Mega number...the odds of winning that are 1 in 41,416,353. The more difficult it is to win, the larger the jackpot will become. When it gets high enough there's usually a ticket buying frenzy.

So, "choose" your lotto numbers carefully, and wish me luck as I attempt to crack my "permutation" lock.

Interesting days

Today - Go For A Ride Day

Tomorrow- Thanksgiving Day and Fibonacci Day

Next Wednesday - Electronic Greetings Day and Square Dancing Day

December 22 - Date Nut Bread Day and Forefathers' Day