5 of 5 Items .... Type: Combinatorics

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You know the song. "And a Partridge in a Pear tree." What patterns of numbers can we find here?

The first partridge.

If you look at the total gifts each day, what sequence of numbers is this?



Four Calling Birds, calling out numbers ...

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Consider eight objects. We will choose them one at a time, two at a time, three at a time, and so on.

Which of these will result in identical numbers of ways?
Why?

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The cast of a school play that requires 4 girls and 3 boys is to be selected from 7 eligible girls and 9 eligible boys.

Will it be a different calculation if the boys are willing to play girls' parts, as in Shakespeare's time? If so, how will it be different?

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I found this book, Making Faces, the other day in a storage box. There are eight faces, and each face is divided into five tabs (head or hat, eyes, nose & cheeks, mouth, and shirt). You can flip any of the face pieces to any of the eight versions.




Here's the back cover.




What do you think of that claim?
"You can make more than 65,000 other faces by mixing the pages of this book."

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Wowie Wednesday....

There are more ways to arrange a regular deck of cards than atoms on our planet. Shuffle a deck of cards thoroughly and pile them up.

No one has, and no one likely will ever, hold the exact same arrangement of those 52 cards that you have in your hand right now.