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Slide 2

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Chapter 5 - Arrangements…read more

Slide 3

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Arrangements
· How many different ways are there of arranging the
letters A, B and C?
Solution 1: Solution 2:
Write out all the possible There are 3 places to fill:
permutations:
- A can go in any of the 3 spaces
· ABC - B can go in any of the 2 that are left
· ACB - C can go in the last place
· BAC 6 ways
· BCA 3 x 2 x 1 = 6 ways
· CAB
· CBA
The ORDER IS Important…read more

Slide 4

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Basic understanding (!)
· How many different ways are there of arranging the letters A,
B C, D and E?
There are 5 places to fill:
___ ___ ___ ___ ___
- A can go in any of the 5 spaces
- B can go in any of the 4 that are left
- Etc...
5 x 4 x 3 x 2 x 1 = 120 ways
Consecutive numbers that are multiplied together can be
done using the ! (factorial) button
5 x 4 x 3 x 2 x 1 = 5!…read more

Slide 5

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Practise questions
· How many different ways are there of arranging the letters on
the following eight cards?
A B C D E F G H
· The digits below form a 6 digit number. How many different
6-digit numbers can be formed?
1 2 3 4 5 6
· Four bricks are arranged in a line. How many different
possible arrangements of the colours are there?
orange blue green purple…read more

Slide 6

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Repeated objects
· How many different ways are there of arranging the letters on
the following eight cards?
A A A B C C C C
There are 8! Ways of arranging the letters but many will be the
same because some letters appear more than once
To get rid of duplicates, we cancel the repetitions
8! (8 ways in total) 40,320 280 =
= =
3! 4! (3 A's and 4 C's) 144…read more

Slide 7

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Slide 8

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Slide 9

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Slide 10

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Comments

Andrew H

The answer on slide 9 question f i think is wrong, and should read = (3!3!x2) + (3!3!x1)

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