Question

Calcule os números binomial.

Answer 1

Resposta:

Explicação passo-a-passo:

a)

$\binom{5}{2}+\binom{7}{0}=\frac{5!}{2!(5-2)!}+\frac{7!}{0!(7-0)!}=\frac{5.4.3!}{2!.3!}+\frac{7!}{1.7!}=\frac{20}{2.1}+1=10+1=11$

b)

$\binom{7}{7}+\binom{6}{1}=\frac{7!}{7!(7-7)!}+\frac{6!}{1!(6-1)!}=\frac{7!}{7!0!}+\frac{6!}{1!5!}=1+\frac{6.5!}{1.5!}=1+6=7$

c) Como vimos, $\binom{6}{1}=6$ e $\binom{7}{0}=1$. Logo,

$\binom{3}{1}=3$ e $\binom{3}{0}=1$ e $\binom{7}{8}$ não existe, visto p = 8 > n = 7. Assim, temos que

$\binom{7}{8}+\binom{3}{1}+\binom{3}{0}=3+1=4$

d)

$\binom{9}{0}+\binom{9}{1}+\binom{9}{2}+...+\binom{9}{9}=2^{10}=1024$.