1 Table Scenario

This guide is to help you nail your exams in statistics, so let’s dive right in.

In problems like these, divide your thinking into 2 parts:

1. From a group of how many people in total we are choosing a specific number

2. Then we need to sit them.

Let’s say we have 8 people in total. In how many ways can we sit them at a round table?

Step1: Choose how many people you want to sit

So here is 8C8 because out of 8 people we are choosing 8 to sit.

Step2: Sit them

There are 2 things that happen here:

1. we have 8P8 or 8!. This means that we sit the first person, then we have 7 and so on

But the difference from round tables and typical straight sequences is that we can also rotate them around 7 sits (think of this like a clock) So what you do is: 8!/8

Final Answer:

8C8 * 8P8 / 8

2 Table Scenario

Let’s say we have 16 people and 2 tables in total. In how many ways can we sit them at a round table when we want 10 at the first table and 6 at the second?

Step1: Choose how many people you want to sit

So here is 16C10 for the first table and 6C6 for the second table. In other words, out of 16 people wa want 10 for the first table, and the remaining 6 we want them at the second table.

Step2: Sit them

So here, is the same thing, but with two tables.

The first table we have 10 people so 10P10 / 10 and for the second table we have 6P6/6

Final Answer:

(16C10* 10P10/10) *( 6C6*6P6/6)