Number of Possible Telephone NumbersDate: 7/15/96 at 21:23:43 From: Anonymous Subject: Number of Possible Telephone Numbers How many phone numbers can be made under the following conditions: (First digit cannot be 0 or 1 because you'll get the operator or long distance.) a) The first two digits are 3 followed by 6 b) The third digit is even c) The fourth digit is greater than 5 d) The fifth and seventh digits are odd e) The sixth digit is 2 Date: 7/15/96 at 22:1:32 From: Doctor Sydney Subject: Re: Number of Possible Telephone Numbers Hello! This is a great question, and it is from an area of math called combinatorics, which is a fancy way to say "counting." There are people who make their livings thinking about counting problems! One way to approach problems like these is to count and see how many choices we have for each digit and then multiply them together. Assuming that you are talking about 7 digit phone numbers, we note the following: 1) For the first digit, we have only one choice -- we must choose a 3. 2) For the second digit, we have only one choice -- we must choose a 6. 3) For the third digit, we have five choices -- we can choose 0, 2, 4, 6, or 8. 4) For the fourth digit, we have four choices -- we can choose 6, 7, 8, or 9. 5) For the fifth digit, we have five choices -- we can choose 1, 3, 5, 7, or 9. 6) For the sixth digit, we have one choice -- we must choose 2. 7) For the seventh digit, we have five choices -- we can choose 1, 3, 5, 7, or 9. Okay, that said and done, we can solve the problem. Actually, why don't we solve an easier problem, and then armed with the techniques for solving that similar problem and given the above information, you should be able to solve this problem on your own. Okay, so let's think about this problem: How many different license plates can be made with only two "digits" where the first "digit" is a letter, and the second "digit" is a number? So, license plates that look like the following qualify: G9, U2, A1, etc... License plates not qualifying include the following: 9G (Here the number is first whereas the letter should really be first), 88 (no letter), rt355 (too long!). Okay, I think you have the idea. So, let's again look at the choices we have: 1) For the first "digit" we have 26 possibilities -- the 26 letters of the alphabet. 2) For the second "digit" we have 10 possibilities -- 0, 1, 2, ...,9. Let's do the counting in several stages: Suppose the first digit is an "A." Since there are 10 possibilities for the second digit, we have 10 possibilities for license plates beginning with the letter "A." Similarly, for every other letter, there are 10 possibilities for license plates beginning with that letter. Since there are 26 letters, and for each letter we have 10 possible license plates, there are a total of 26*10 = 260 possible license plates. Okay, so one problem is solved. But, you say, THAT wasn't MY question. Well, it wasn't, but I hope that it will help you to answer your question. Using strategies from the second problem, and the setup I gave you for your problem, why don't you see if you can solve your problem. If you want to check your answer and reasoning, please write back! Hope this helps, and good luck. You can tell all of your friends at school that you are a combinatorist (that is a fancy way for saying someone who does these counting problems!). -Doctor Sydney, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 7/16/96 at 21:54:27 From: Anonymous Subject: Dr.Sydney (I Solved it!) Thanks for helping me with that question, my answer is 500 phone numbers. I'm sure it's right. I got it by doing this: 1 X 1 X 5 X 4 X 5 X 5 = 500 possible numbers. Connie Date: 7/17/96 at 15:2:57 From: Doctor Sydney Subject: Re: Dr.Sydney (I Solved it!) Dear Connie, Great job! You did it perfectly. I hope you continue to find fun math problems to work on, and feel free to write us again if you have any questions or things you are curious about! -Doctor Sydney, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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