Aeight-digit code is used to distinguish between different regions. the code uses numbers between 1 and 9, inclusive. a. how many different codes are available for use? (assume that any eight-digit number can be used as a code.) b. the first three digits of a code for a particular region are 113. if no other region has these first three digits as part of its code, how many codes can exist in this region?

a.  

b.  

Explanation:

Part a

In part a since all the eight digits for the code is to be filled using numbers between  1 and 9. Therefore one digit can have 9  different values, and since there are total 8 digits to be filled.

Therefore total number of different code available for the region will be .

Part b

In part b out of eight digits three digits have fixed values i.e. 113. Thus in total there are 5 digits to be filled where each digit can take 9 different value. Therefore, in a region where first three digits of eight digit code are fixed, total number of codes that can exists will be .

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