Seven cards show the letters: A, A, A, A, B, B, C. Cards are chosen at random.

One card is chosen. Find the probability it:

(a(i)) shows A; [1]

(a(ii)) shows A or B; [1]

(a(iii)) does not show B. [1]

Two cards are chosen without replacement. Find the probability:

(b(i)) both show A; [2]

(b(ii)) their letters are different. [3]

(c) Three cards are chosen without replacement. Find the probability none shows C. [2]