what if binary had three states like {0,1,2} instead if {0,1} then how many possible combinations we could have?

Question

so if binary can hold two states i.e {0,1} then total combinations we could get is 2^n. what if binary had three states {0,1,2} then what should be formula? 3^n?

Answer 1

Well, in that case it is not called binary, but ternary. Think as follows:

For a word with $n-$letters you have $3$ possible choices for the first letter, $3$ for the second, $3$ for the third etc. So, since you have $n$ terms you have in total: $$\underbrace{3\cdot3\cdot3\dots3}_{n\text{ times}}=3^n$$

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