Math CentralQuandaries & Queries


Question from KiranReddy:

Hi Team ,
Please help me here ,

i have a requirement that, i need to generate 8 digit word [mix of 26 small letters and 0-9 digits , both are repeatable]
Please give me the count of such words we can generate



You have a total of $26 + 10 = 36$ characters and you want to form 8 character words. Think about making a list of all the 8 character words. Start with one character words. There are 36 of them. Each of them can be expanded to a two character word by appending a second character. Since there are 36 possibilities for the second character you have $36 \times 36 = 36^2$ two character words.

Each of the $36^2$ two character words can be expanded to a three character word by appending a third character. Hence there are $36^2 \times 36 = 36^3$ three character words.

And so on,

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