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We usually write numbers in decimal form (or base 10), meaning numbers are composed using 10...

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Advance Math

We usually write numbers in decimal form (or base 10), meaningnumbers are composed using 10 different “digits” {0,1,...,9}.Sometimes though it is useful to write numbers in hexadecimal orbase 16. Now there are 16 distinct digits that can be used to formnumbers: {0,1,...,9,A,B,C,D,E,F}. So for example, a 3 digithexadecimal number might be 3B8. (a) How many 2-digit hexadecimalsare there in which the first digit is E or F? Explain your answer interms of the additive principle (using either events or sets). (b)Explain why your answer to the previous part is correct in terms ofthe multiplicative principle (using either events or sets). Why doboth the additive and multiplicative principles give you the sameanswer? (c) How many 3-digit hexadecimals start with a letter (A-F)and end with a numeral (0-9)? Explain. ( d) How many 3-digithexadecimals start with a letter (A-F) or end with a numeral (0-9)(or both)? Explain.

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