Systematic listing and counting

Kwame has 4 shirts and 3 pairs of shorts, all different. How many different outfits (one shirt and one pair of shorts) can he make?

From Farida's village there are 3 paths down to the river, and from the river 4 roads to the market. A route is one path followed by one road. How many different routes are there from the village to the market?

A canteen offers 2 soups, 3 main dishes and 2 drinks. A meal is one soup, one main dish and one drink. How many different meals are there?

Lerato has red, blue and yellow T-shirts and black and brown trousers. She calls out: red–black, blue–brown, red–brown, yellow–black, blue–black. Then she says, "I can't think of any more, so that's all of them." What is the best reply?

Using the digit cards 1, 5 and 7 (each card at most once), list every two-digit number you can make. Write them separated by commas, like {12, 34}.

Mei has 4 different books to put in a row on a shelf. In how many different orders can she arrange them?

Six friends meet, and every two of them shake hands exactly once. How many handshakes are there?

In a chess club in Nairobi, 8 players each play every other player exactly once. How many games are played?

In Lean, pairs as bs is the organised list of all pairs from a list as of first choices and a list bs of second choices. Which Lean statement says the product rule?

Complete outfits(tops, bottoms) so that it returns a list of every pair (top, bottom), each exactly once. Use the system from the lesson: one loop for the tops, and inside it a loop for the bottoms.