Retain the exceptional all-blue score in the conditional game

A box contains 2 red balls,3 green balls and x blue balls, with integer $x\ge5$. A contestant chooses 5 balls without replacement. S is the number of green balls plus three times the number of red balls. Blue balls score nothing unless all 5 balls are blue, in which case S=25.

(i) Show that $P(S=6)=\dfrac{20x(x^2-3x+14)}{(x+5)(x+4)(x+3)(x+2)(x+1)}$.2 marks

(ii) Given $P(S=6)=5/63$, calculate x.2 marks

(iii) Complete the distribution table.4 marks

s	Given $P(S=s)$
1	to find
2	$5/42$
3	$5/63$
4	to find
5	$5/21$
6	$5/63$
7	to find
8	$5/84$
9	$1/252$
25	to find

(iv) Evaluate $E(S)$ and find $P(S>E(S))$.2 marks

(v) Find the probability that no green balls are drawn, given $S>E(S)$.2 marks