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A four or fivedigit PIN is to be selected from the nine digits 0,1,2,3,4,5,6,7,8. 1. How many 4-digit PINs are possible if: a) all 4

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A four or fivedigit PIN is to be selected from the nine digits 0,1,2,3,4,5,6,7,8. 1. How many 4-digit PINs are possible if: a) all 4 digits are the same? eg. 8888 l b) no digit can be repeated?' l C} any digit can be repeated?' l d) the rst 2 digits must be ditterent digits and the last 2 digits must be the same, but none of the first 2 digits can be used in the last 2? 2. Suppose any digit can be repeated, how many 4-digit Ple are possible it each PIN: a} must end with "2"? l l b) must not start with "1"? 5} must neither start with "5" nor end with "5"?l 3. Suppose no digit can be repeated, how many 5-digit PINs are possible if each PIN: a} must end with "2"? l l b) must not start with "1"? (2} must neither start with "5" nor end with "5"?l

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