A set of three letters {a,b,c}, where ordering matters. The length is defined as the number of letters the string contains.

Question

a) How many strings of length 4 can you create?

b) How many strings of length 4 do not have consecutive characters being the same?

c) How many strings of length 4 contain neither "cab" nor "bac", or do not have consecutive characters being the same?

What i've done

a) $3^4 = 81$

b) First letter = 3 choices. Second letter onwards = 2 choices.

Thus $3 * 2^3 = 24$

c)

"cab"

Can be considered as a string with 2 characters however cab can't repeat. Thus

$3P2 = 6$

"bac"

Can be considered as a string with 2 characters however bac can't repeat. Thus

$3P2 = 6$

Hence from above, answer is $24 - 8 = 16$ ( 8 not 12 because 'ccab' 'cabb' 'bbac' and 'bacc' have been excluded.)

Is there any error in my calculations?

edit: Tagged Pic of question