Kombinační číslo: Porovnání verzí

Pro přirozená čísla ''n'' a ''k'', kde <math> 0 \le k \le n </math> platí

:<math>{n \choose k} = {n \choose {n-k}},</math>

:<math>{{n} \choose {1}} = n,</math>

:<math>{{n} \choose {0}} = {{n} \choose {n}} = 1,</math>

:<math>{n \choose {k+1}} = {n \choose k}\frac{n-k}{k+1},</math>

:<math>{{n+1} \choose {k}} = {n \choose k}+{n \choose {k-1}},</math>

:<math>{{n-1} \choose {k-1}} + {{n-1} \choose {k}} = {n \choose {k}},</math>

:<math>\sum_{i=k}^n {i \choose {k}} = {n+1 \choose {k+1}},</math>

:<math>\sum_{i=0}^n {{k+i} \choose {i}} = {k+n+1 \choose n},</math>

:<math>\sum_{i=0}^n {n \choose {i}} = 2^n,</math>

:<math>\sum_{i=0}^n (-1)^i{n \choose {i}} = 0,</math>

:<math>\sum_{i=0}^n {n \choose {i}}^2 = {2n \choose {n}}.</math>