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Every teacher at a high school is given a n-digit code, e.g. 530...297 (n digits in...

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Advance Math

Every teacher at a high school is given a n-digit code, e.g.530...297 (n digits in total).

(1) How many different codes are there?

(2) How many codes read the same backward and forward? (Considerthe cases where n is odd or even.)

(3) How many codes contain odd digits only?

(4) How many codes contain at least one even digit?

(5) Consider the case where n is 6. How many codes have distinctdigits? (That is, no digit appears more than once.)

Answer & Explanation Solved by verified expert
4.1 Ratings (731 Votes)
1 In a ndigit code every digit is chosen from0123456789 So each digit can be chosen in 10 ways andhence n digits can be chosen in ways Thereforethere are differentcodes2 First suppose n is even Let n2k Then we can choose firstk digits in any way but the last k digits will    See Answer
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