File:5-choose-3 tree proof.svg
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Captions
Captions
Proof for combination using tree and rule product
Summary
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| 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 | 01:32, 9 October 2021 | | 906 × 689 (1.89 MB) | Guy vandegrift (talk | contribs) | white background |
| 17:14, 4 October 2021 |  | 906 × 689 (1.89 MB) | Guy vandegrift (talk | contribs) | Uploaded own work with UploadWizard |
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