Number and Letter CombinationsDate: 07/29/97 at 20:25:38 From: chad chilcot Subject: Possible number combinations I have a question concerning number calculations. How many possible combinations can a person make with letters (lower case) a-z and 1-9; starting from 1 digit and ending up with up to 8 digits? For example az3 or 1d or ae4rg or 5634f45. How did you figure it out - what formula did you use? Thanks. Date: 07/30/97 at 05:50:19 From: Doctor Anthony Subject: Re: Possible number combinations First consider the number of combinations when no repetition of letters or numbers is allowed. I will use the notation nCr to represent the number of combinations of r things that can be formed from n things. For example, 9C4 is the number of combinations of 4 things that can be made from 9 things 9 x 8 x 7 x 6 The value of 9C4 is --------------- = 126 1 x 2 x 3 x 4 9! It can also be calculated from ------ 4! 5! Using this notation the answer to your question is easily given. There are 26 letters and 9 numbers giving 35 things from which to choose. These can then be chosen in combinations ranging in size from 1 to 8 in the following number of ways: 35C1 + 35C2 + 35C3 + 35C4 + 35C5 + 35C6 + 35C7 + 35C8 = 35 + 595 + 6545 + 52360 + 324632 + 1623160 + 6724520 + 23535820 = 32267667 This is the answer when no repetition of letters or numbers is allowed. If repetitions are allowed then the calculation is simpler, since we can choose every position of a combination of size, say 3, in 35 ways, giving 35^3 combinations. For combinations of size 1 to 8, the total is 35 + 35^2 + 35^3 + 35^4 + 35^5 + 35^6 + 35^7 + 35^8 = 2.31810702... x 10^12 -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 07/31/97 at 00:18:27 From: Ann Subject: Re: Possible number combinations Thank you very much! |
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