1. Consider the two dierent methods for computing the number of 4-digit pins (wh

Question

1. Consider the two dierent methods for computing the number of 4-digit pins (where each digit may either be a number (0-9) or a letter (a-z)) where at least 1 digit must be an 8. Method 1: There are 4 positions in which the 8 can go hence we can rst choose where the 8 goes. (there are 4 such choices). Then we can choose the other digits to be any digit (there are 36 possibilities for each of these three digits). Hence the total number of such 4 digits pins is 4·36·36·36 = 186624.

Method 2: There are 364 total possible pins (which may or may not contain a 8), and the number of pins which do not contain an 8 is 354. Thus the total number of pins that contain an 8 can be derived through the dierence rule as 364 354 = 178991. Since we have dierent results only one (or perhaps neither) of these results is correct. Which method gives the correct number of such pins and explain what is wrong with the other method.

Explanation / Answer

Method 2 will give correct output. Method 1 will count duplicate cases as well. e.g 8812 will be counted twice.

Method 2 ensure that we dont count same case twice.

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