a How many 6 character strings using letters az and numbers

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

Solution

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

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