Happy Telephone Numbers Day! You may be surprised to learn that these aren't the telephone numbers associated with our individual telephones, but instead represent the number of ways that n number of telephones can be connected to each other for 2-way calls. For example, if you have 0 phones or 1 phone, there only 2-way "connection" possible is no connection at all. But if you have 2 phones, there are now 2 possibilities: no connection at all or the 2 phones connected to each other. This table shows the number of combinations possible when you have very few phones: You might notice that the number of combinations starts very small but then grows pretty quickly. This is one reason why it's impractical to set up a telephone network with equipment dedicated to every possible phone call combination. Actually writing and counting all those combinations would get tedious pretty quickly; fortunately there's a formula for that: Applying this formula, you can see just how
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