Rods are produced in two lengths, called 'short' and 'long'. S is the length, in centimetres, of a short rod, where S N(5, 0.25). L. is the length, in centimetres, of a long rod, where L N(10, 1). Rods are joined to give longer lengths. Find the probability that a length consisting of

(a) two short rods and four long rods is longer than 52 cm,

(b) three short rods and two long rods is between 33 cm and 36 cm long.

(c) six short rods is longer than a length consisting of three long rods.