If you look at the 4th and 5th grade problem, you would see that John Kerry needed to visit 3 places instead of 49 cities. One way of thinking about the answer to that problem is to say, Kerry has 3 ways to choose the first city to visit. Once he has made that choice, he has 2 ways to decide where to go next and finally 1 way to choose the last city to go to. To find the total number of ways, you multiply 3 X 2 X 1 which equals 6.
Now we apply that technique to this problem, there are 49 ways to choose the first city, 48 ways to choose the second city, 47 ways to choose the third city, and so forth until there is just 1 way to choose the forty-ninth city. Then you need to multiply all forty-nine numbers to get the answer: 49 X 48 X 47 X 46 X 45 X ... X 4 X 3 X 2 X 1. If you try to do this on a calculator, you will need a scientific calculator because the answer has 63 digits! It is written 49! and called 49 factorial. It is approximately equal to 608,281,864,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 ways.
The second question was how long would it take to write out all these different orders, taking one second to write each one. If you convert 608,281,864,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 seconds into years by dividing by 60, 60, 24 and 365.25, you get a 56 digit answer: 19,275,289,120,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years. Needless to say, you will not finish this in your lifetime and definitely not before Kerry needs to plan his campaign tour! |
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