Homework Answers
Suppose, we have to form a word of length 10 characters wide and we have to use only a,b,c,...., z. Then there are 10 positions to be filled by the given characters. No of characters given in this example is 26. It means we can fill each position in 26 different ways. So, to find total no of ways all positions can be filled we will multiply 26 as many times as the length of word, in this case, 10. So we sill multiply 26 10 times. So total number of words will be 26*26*...*26 10 times, which will be 2610. This same logic has bee used in following table. This was just an explanation.
| 4 characters | 8 characters | 12 characters | |
| Only numbers (There are 10 numbers 0 through 9) |
Total = 10*10*10*10 = 10000 |
Total = 10*10*...*10 8 times = 108 |
Total = 10*10*.....*10 12 times = 1012 |
| Only lower case letters (26 letters, a through z) |
Total = 26*26*26*26 =264 |
Total = 26*26*....*26 8 times = 268 |
Total = 26*26*.....*26 12 times = 2612 |
| Only lowercase letters and numbers (26 + 10 = 36 distinct characters) |
Total = 36*36*36*36 = 364 |
Total = 36*36*....*36 8 times = 368 |
Total = 36*36*....*36 12 times = 3612 |
| Only numbers, lowercase letters and upper case letters (10 +26 + 26 = 62 distinct characters) |
Total = 62*62*62*62 = 624 |
Total = 62*62*....*62 8 times = 628 |
Total = 62*62*....*62 12 times = 6212 |
| Numbers lowercase letters , uppercase letters and visible punctuation (10+26+26+32 = 94 distinct characters) |
Total = 94*94*94*94 = 944 |
Total = 94*94*....*94 8 times = 948 |
Total = 94*94*....*94 12 times = 9412 |
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