Question:

(a) Find the number of different words which can be formed with the letters A, A, A, B, B, C, C if

(i) there is no restriction
(ii) they must start and end with different letters
(iii) the A's must be together
(iv) the A's must be together and the B's must not be together

(b) (i) In how many ways can 5 balls be selected from 7 red balls and 4 black balls?

(ii) How many of the selections of 5 balls have a majority of black balls?

(iii) Find the probability that if 5 balls are selected at random from a bag containing 7 red balls and 4 black balls, there is not a majority of black balls.