Paskal üçburçlugy

Paskal üçburçlugyň ilkinji 15 setiri (n = 0, 1, …, 14)

Binomial koeffisientler we Paskal üçburçlugy şeýle bolsa,

$(x+y)^{n}=\sum _{k=0}^{n}{n \choose k}x^{n-k}y^{k}$$(x+y)^{n}=\sum _{k=0}^{n}{n \choose k}x^{n-k}y^{k}$

onda

${n \choose k}={n-1 \choose k-1}+{n-1 \choose k}$${n \choose k}={n-1 \choose k-1}+{n-1 \choose k}$ bolar.

Formula

${n \choose k}={\frac {n!}{k!\cdot (n-k)!}}={\frac {n}{1}}\cdot {\frac {n-1}{2}}\cdot \ldots \cdot {\frac {n-k+1}{k}}$${n \choose k}={\frac {n!}{k!\cdot (n-k)!}}={\frac {n}{1}}\cdot {\frac {n-1}{2}}\cdot \ldots \cdot {\frac {n-k+1}{k}}$, $n,k\in \mathbb {N} _{0}$$n,k\in \mathbb {N} _{0}$ bolsa

Meselem

${5 \choose 3}={\frac {5!}{3!\cdot 2!}}={\frac {5\cdot 4\cdot 3!}{2!\cdot 3!}}={\frac {5\cdot 4}{2!}}={\frac {20}{2}}=10$${5 \choose 3}={\frac {5!}{3!\cdot 2!}}={\frac {5\cdot 4\cdot 3!}{2!\cdot 3!}}={\frac {5\cdot 4}{2!}}={\frac {20}{2}}=10$