F.5 trigo& probability

17(a) C(16,2) = 120

C(x,2)/120 < 1/12

x(x - 1) < 20

=> x = 2,3,4

(b) Take x = 4

The probability = C(4,3)/C(16,3) + C(4,2)C(12,1)/C(16,3) = 19/140

13 1/(tanx)^2 + 4/tanx - 21 = 0

21y^2 - 4y - 1 = 0 (where y = tanx)

(3y - 1)(7y + 1) = 0

y = 1/3 or -1/7

x = 18 or 172