Problems

Downtown MathHattan has a grid pattern, with \(4\) streets going east-west and \(6\) streets south-north. You take a taxi from School (A) to cinema (point B), but you would like to stop by an ice cream shop first. In how many ways can a taxi get you there if you don’t want to take a route that is longer than necessary?

Gabby the Gnome has \(3\) cloaks of different colours: blue, green, and brown. He also has \(5\) different hats: \(3\) yellow and \(2\) red. Finally, he owns \(6\) different pairs of shoes: \(2\) yellow, and \(4\) red. Gabby is selecting an outfit: a cloak, a hat, and a pair of shoes. In how many ways can he do it if he wants the colour of his shoes to match the colour of the hat?