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?

An inventor claims to have developed a reversed heat engine (ie. a heat pump) which is able to deliver 10 kj heat into the room at 20°c from outside ambient temperature of -10°c by consuming only 2 kj electricity in winter. this claim is a)-impossible b)-possible only if the heat pump is ideal c)-practically possible d)-unable to be assessed as it depends on the working fluid used in the heat pump.