b How many flags have five different colours? c How many flags look the same if flipped top to bottom or side to side? d How many flags look the same if flipped about either diagonal?

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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please answer only parts b, c, and d as i have already answered part a. can you please provide an explanation too, so i can understand the answer

12 Many Flags
5. Ca
Consider a square flag which is divided into five regions like this:
123451-345
25
5
4.5
the regions. Each region has only one colour. Two, three, four, or five
Up to five colours, red, white, green, blue, yellow, are used to colour
regions may have the same colour. Here are three examples:
Each flag is designed so that it can be hung on a wall with two sides
vertical. The regions are shaped so that, when all regions have the same
colour, the flags are symmetrical horizontally, vertically, diagonally, and
rotationally about their centre through 90°, 180°, and 270°.
a How many flags have four colours with the top-left and bottom-right
colours the same?
b How many flags have five different colours?
c How many flags look the same if flipped top to bottom or side to side?
d How many flags look the same if flipped about either diagonal?
Transcribed Image Text:12 Many Flags 5. Ca Consider a square flag which is divided into five regions like this: 123451-345 25 5 4.5 the regions. Each region has only one colour. Two, three, four, or five Up to five colours, red, white, green, blue, yellow, are used to colour regions may have the same colour. Here are three examples: Each flag is designed so that it can be hung on a wall with two sides vertical. The regions are shaped so that, when all regions have the same colour, the flags are symmetrical horizontally, vertically, diagonally, and rotationally about their centre through 90°, 180°, and 270°. a How many flags have four colours with the top-left and bottom-right colours the same? b How many flags have five different colours? c How many flags look the same if flipped top to bottom or side to side? d How many flags look the same if flipped about either diagonal?
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