Question

calcule o valor de E sendo

Answer 1

O número binomial $\binom{n}{p}$ é definido como

$\binom{n}{p}=\frac{n!}{p! \cdot \left(n-p \right )!}$


Sendo assim

$E=\binom{5}{2}+\binom{6}{1}+\binom{7}{7}+\binom{5}{3}\\ \\ =\frac{5!}{2!\cdot\left(5-2 \right )!}+\frac{6!}{1!\cdot\left(6-1 \right )!}+\frac{7!}{7!\cdot\left(7-7 \right )!}+\frac{5!}{3!\cdot\left(5-3 \right )!}\\ \\ =\frac{5!}{2! \cdot 3!}+\frac{6!}{1! \cdot 5!}+\frac{7!}{7! \cdot 0!}+\frac{5!}{3! \cdot 2!}\\ \\ =\frac{5 \cdot 4 \cdot 3!}{2 \cdot 1 \cdot 3!}+\frac{6 \cdot 5!}{1 \cdot 5!}+\frac{7!}{7! \cdot 1}+\frac{5 \cdot 4 \cdot 3!}{3! \cdot 2 \cdot 1}\\ \\ =\frac{5 \cdot 4}{2 \cdot 1}+ \frac{6}{1}+\frac{1}{1}+\frac{5 \cdot 4}{2 \cdot 1}\\ \\ =10+6+1+10\\ \\ =27$