What is a permutation?

What is the permutation of { }?

{ }

What is the permutation of {1}?

{1}

What is the permutation of {1, 2}?

• {1, 2}
• {2, 1}

What is the permutation of {1, 2, 3}?

• {1, 2, 3}
• {1, 3, 2}
• {2, 1, 3}
• {2, 3, 1}
• {3, 1, 2}
• {3, 2, 1}

Which of them start with 1?

• {1, 2, 3}
• {1, 3, 2}

What are the rest of these elements?

• {2, 3}
• {3, 2}

Do they resemble something?

• No

What about the permutation of {2, 3}?

• Yes

What is append x on {y, z}?

• {x, y, z}

What is append x on each of {y, z}?

• {x, y}
• {x, z}

Can we say the permutation of {1, 2, 3} = {append 1 on each permutation of {2, 3}}, {append 2 on each permutation of {1, 3}}, {append 3 on each permutation of {1, 2}}?

• That’s a mouthful.

What is {append 1 on each permutation of {2, 3}}?

• {append 1 on each permutation of {2, 3}}
• {append 1 on each {{2, 3}, {3, 2}}}
• {{1, 2, 3}, {1, 3, 2}}

What about {append 2 on each permutation of {1, 3}} and {append 3 on each permutation of {1, 2}}?

• {{2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}}

What do we get when we combine them all?

• {{1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}}
• i.e., permutation of {1, 2, 3}

Do you know what a permutation is now?

• Yes

Did you have fun?

• Go have some cookies.

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