A bowl contains 15 red balls, 20 green balls and 12 blue balls. A woman selects balls at random without looking at them. How many balls must she select to be sure of having at least three balls of the same color?

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.