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Combinatorics with Factorials

Goal

Learn about factorial-based problems (number of permutations of N distinguishable objects).
Learn how to distinguish them from other types of problems.
Note: this topic was one of the most challenging ones in the year.

Easy Problem (#1)

You have 3 Lego bricks in different colours. You stack all 3 to make a tower.

How many different towers can you build?

Medium Problem (#2)

A chef makes a cake with 4 different layers: chocolate, raspberry, blueberry and vanilla. Each layer is used once.

How many different layer orders are possible?

Medium Problem (#5)

A practice section of Primary Mathematics Challenge has 3 questions. Each question has exactly 5 options: A, B, C, D or E.

How many different ways can the test be answered?

Hard Problem (#8)

A football team has 11 children.

They choose a captain and a vice-captain.

How many different choices are possible?

In Real Life