In a learning task, a subject is presented with five buttons. He must learn to press three specific buttons in a predetermined order. What chance does that subject have of pressing correctly on the...

In a learning task, a subject is presented with five buttons. He must learn to press three specific buttons in a predetermined order. What chance does that subject have of pressing correctly on the first trial?

An ice-cream shop has six different flavors of ice cream, and you can order any combination of any number of them (but only one scoop of each flavor). How many different icecream cone combinations could they truthfully advertise? (We do not care if the Oreo Mint is above or below the Raspberry-Pistachio. Each cone must have at least one scoop of ice cream—an empty cone doesn’t count.)