Circular and Linear Arrangements

Circular and Linear Arrangements

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains how to arrange six people in a circular fashion, contrasting it with linear arrangements. It highlights that while linear arrangements use six factorial, circular arrangements use 'N minus 1' factorial due to the rotational symmetry of circles. The tutorial emphasizes understanding the concept over memorization, providing a detailed explanation of why the first person has only one seating option in a circle, unlike in a row.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many ways can six people be arranged in a row?

6

120

720

36

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the formula for arranging 'N' people in a circle?

N factorial

N minus 1 factorial

N plus 1 factorial

N divided by 2 factorial

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why do we subtract one from 'N' in circular arrangements?

To make calculations easier

To account for symmetry

To match linear arrangement

To reduce complexity

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many slots are available for the first person in a linear arrangement of six people?

5

6

7

4

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In a linear arrangement, how many ways can the second person be seated after the first?

4

6

3

5

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the common misconception about seating the first person in a circular arrangement?

They can be seated in six ways

They can be seated in four ways

They can be seated in one way

They can be seated in five ways

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is the view the same for the first person regardless of the chair in a circular arrangement?

All chairs are identical

The table is small

The circle is symmetrical

The chairs are numbered

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