Timeline for Proving Pascal's Rule : ${{n} \choose {r}}={{n-1} \choose {r-1}}+{{n-1} \choose r}$ when $1\leq r\leq n$
Current License: CC BY-SA 2.5
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| Aug 11, 2018 at 22:14 | comment | added | Mosab Shaheen | Thanks! but in the second case "Similarly, the number of ways of having no red balls is to choose all the balls as blue balls which can be done in C(n−1,r) ways", according to what you mentioned it should be C(n,r) not C(n−1,r). Could you please elaborate more on this idea. | |
| Feb 5, 2011 at 0:14 | comment | added | user17762 | @Christopher: More generally, any equality involving only natural numbers can be argued purely on the basis of counting. | |
| Feb 5, 2011 at 0:06 | history | edited | user17762 | CC BY-SA 2.5 |
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| Feb 4, 2011 at 23:47 | history | edited | user17762 | CC BY-SA 2.5 |
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| Feb 4, 2011 at 23:36 | comment | added | user6639 | Thanks! I was having a hard time visualizing the concept, and I figured proving this would help. Your example is brilliant. | |
| Feb 4, 2011 at 23:33 | history | edited | user17762 | CC BY-SA 2.5 |
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| Feb 4, 2011 at 23:27 | history | answered | user17762 | CC BY-SA 2.5 |