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 Question from Ali, a student: If I have an app and offer a two, three and four digits name and it can be only number, letters or both? I want to know how many options will I have for each? For example the two digits: aa, 11, a1 or 1a the three digits: 111, a2a, 222 the four digits: 1111, 2ge3 or 1234 So if I used all the letters and all the numbers but nothing starts with a zero How can I calculate them separately? Or what's the result for each? Thank you Ali

Hi Ali,

I am going to call these strings of characters. You want strings of length 2, 3 and 4 and you have $10+26 = 36$ characters. Write each string starting with the leftmost character, which can't be zero so you have 35 choices for the first character, or in other words 35 one character strings.

Each of these one character string can be extended to a two character string by appending one character on the right. There are 36 characters to choose from so each one character string can be extended to 36 two character strings and hence there are $35 \times 36$ two character strings.

Each of these two character string can be extended to a three character string by appending one character on the right. How many three character strings are there?

Penny

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