Courtesy:Munsang College HK Island

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CourtesyMunsang College(HK Island)

• Introductory Combinatorics
• Translated July 2001
• Scroll down to advance
• (Note Retaining mathematical correctness is the
  translators foremost goal.)

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Lets start counting!

• Christmas is just round the corner! The 5 of us
  gave out Christmas cards to each other. When we
  gathered, we exchanged the cards among ourselves
  to look at.

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? 5 20
Doris
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Our Christmas Gathering

• As a friendly gesture, the five buddies in the
  party shook hands with each other.
• How many handshakes were made?

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Heres the diagram we just used in the previous
question.
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4?5?2 10 Use a tree diagram if preferred
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Lets go line up!

• After dessert time, Aaron brought out 3 chairs
  and lined them up, then asked Eric and Ben to be
  seated. A small debate went on until the three
  boys finally sat properly and had a picture taken!

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Ben -- Eric -- Aaron Ben -- Aaron -- Eric Eric --
Ben -- Aaron Eric -- Aaron -- Ben Aaron -- Eric --
Ben Aaron -- Ben -- Eric
And he correctly figured out the number of ways
to be 6
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The camera girls, Doris and Carmen, would not
miss the opportunity and brought their chairs
along. The 5 people shuffled positions and there
came more variations.
How many ways can the 5 persons be lined up
randomly?
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So how many arrangements altogether?
2 ways to occupy the fourth

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Number of arrangements (permutations) 5 ? 4 ? 3
? 2 ?1 120 5!
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Number of permutations for 6 positions 6! 6 ?
5 ? 4 ? 3 ? 2 ?1 720
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The rest of the party were impressed by Bens
love of thinking. Now they tried to challenge
him. Aaron said, I am the class monitor and
should have the privilege to pick first. I want
to pick the middle seat. Everything else is up to
you. Then he asked, Ben, how many possible
arrangements are we going to have?
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4 ? 3 ? 1 ? 2 ? 1 24
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Now that everyone was so involved. Carmen came up
with another challenge Im the youngest in the
group and should deserve some kind of privilege.
I want to sit beside Aaron. Ben, could you
calculate once again?
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6 6 12
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Ben was nearly burned out, and said, You guys
are way too picky, Aaron and Carmen. Why dont
we just move two of the chairs to the front and
let you guys fight for yourselves. The three of
us will sit at the back. And hey, shouldnt it be
your turn to calculate?
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Number of ways to sit 3 people in the back row 3
? 2 ? 1 6
Number of ways to sit 2 people in the Front
row 2 ? 1 2
Total number of arrangements
2 ? 6 12