. A LEGO Problem. A LEGO miniature figure (AKA minifig) consists of 5 parts - a pair of legs, a torso including arms, a head, hair/hat, and an accessory. The LEGO store allows you to build your own custom minifig from a selection of available parts. On a given day, the LEGO store has 4 different pairs of legs, 6 different torsos, 5 different heads, 6 different hair/hats and 8 accessories in stock. Specifically, they have many copies of each part.

(a) How many unique minifigs can be constructed if they must contains all 5 parts?

(b) Unfortunately, you can't just buy one minifig, you must buy them in packs of 3. If you want all 3 of your minifigs to be completely different, how many possible minifig packages could be prepared and sold to lovers of little plastic people? (completely different means none of the parts in one minifig are duplicated in other two

(c) If, amongst the different heads, you note 2 male heads, 2 female heads and 1 robot head, what is the probability that a minifig randomly selected from a pile of completed minifigs is female?