(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

How many (natural) numbers less than 100 contain a 3? (Note: 13, 35 and 73 all

contain a 3 but 42, 65 and 88 do not).

3. The attempt at a solution

Of course I know that the numbers containing a 3 including 10 numbers starting with a 3 (30, . . . 39),and 10 numbers ending in a 3 (3, 13, . . . , 93), with 33 being counted twice, so a total of 19 numbers. I've found this by counting. But is there a quick systematic way of obtaining this answerusing combinations/permutationsetc? Unfortunently my knowledge of combinatorics is very poor, so I appreciate any help.

Between 10 to 100 there are 98 2-digit numbers that can possibly contain a 3 in the 1's or 10's positions... I'm stuck here.

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# Homework Help: Combinations/permutations help

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