a) How many 6 character strings (using letters a-z and numbers 0-9) can be made

Question

a) How many 6 character strings (using letters a-z and numbers 0-9) can be made if we don't restrict the characters, except we do not allow a certain 3 letter word to appear anywhere among the sequnce of characters (like 'cat')?

b) How many 6 character strings can be made if the first three characters start the same?

I was thinking for A that a 3 letter word can occur in 4 different places in a 6 character string. So if I use 'cat', would it be like 1*1*1*36*36*36 or 26*25*24*36*36*36 and then times that by 4. Then subtract that from the total possiblities 36^6 to get the number that don't use that word?

For B I was thikning it would be 1*1*1*36*36*36 and then I would need to multiply that by 36 because there are 36 possible different starting characters

Explanation / Answer

36^6- 1*1*1*36*36*36

B. ( 1*1*1*36*36*36 )*36

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