The letters T, C and A can be written in several different orders. 

a. Write the letters in as many different orders as possible. 

b. If a computer writes these three letters in a random. order, calculate the probability that:

(i) The letters will be written in alphabetical order.

(ii) The letter T is written before both the letters A and C.

(iii) The letter C is written after the letter A.

(iv) The computer will spell the word CAT.