File:5-choose-3 tree proof.svg
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Size of this PNG preview of this SVG file: 788 × 599 pixels. Other resolutions: 316 × 240 pixels | 631 × 480 pixels | 1,010 × 768 pixels | 1,280 × 973 pixels | 2,560 × 1,947 pixels | 906 × 689 pixels.
Original file (SVG file, nominally 906 × 689 pixels, file size: 1.89 MB)
Summary
| Description |
English: Start at the center, with the understanding that 5-choose-3 three is unknown (pretend you can't count the dotted lines.) Letting 5-choose3 equal X include subscripts on 2 Rs and 3 Cs to conclude that their permutations are 2! and 3!, respectively. After both letters have been subscripted and all permutations are counted, we use the product rule to conclude that the outer branches of the tree has (2!)(3!)(X) endpoints. But we also know that this equals the permutation of 5 objects. Hence 5!=(2!)(3!)(X). Solving yields X=10. |
| Date | |
| Source | Own work |
| Author | Guy vandegrift |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 02:32, 9 October 2021 | | 906 × 689 (1.89 MB) | wikimediacommons>Guy vandegrift | white background |
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