A technical manual contains 10 pages of text, 7 pages of diagrams and 3 pages of colour illustrations. Four different pages are selected at random from the manual. Let X be the number of pages of colour illustrations selected.

a. Draw up the probability distribution table for X.

b. Find:

i. E(X)

ii. The probability that fewer than two pages with colour illustrations are selected, given that at least one page with colour illustrations is selected.