a)

$\left(\begin{array}{c}8\\ 5\end{array}\right)=\frac{8!}{5!\cdot 3!}=\frac{5!\cdot 6\cdot 7\cdot 8}{5!\cdot 1\cdot 2\cdot 3}=7\cdot 8=56$  

---

b) 

$\left(\begin{array}{c}8\\ 6\end{array}\right)=\frac{8!}{6!\cdot 2!}=\frac{6!\cdot 7\cdot 8}{6!\cdot 1\cdot 2}=7\cdot 4=28$  

---

c)

$\left(\begin{array}{c}10\\ 2\end{array}\right)=\frac{10!}{2!\cdot 8!}=\frac{8!\cdot 9\cdot 10}{1\cdot 2\cdot 8!}=9\cdot 5=45$  

---

d)

$\left(\begin{array}{c}10\\ 7\end{array}\right)=\frac{10!}{7!\cdot 3!}=\frac{7!\cdot 8\cdot 9\cdot 10}{7!\cdot 1\cdot 2\cdot 3}=4\cdot 3\cdot 10=120$  

---

e)

$\left(\begin{array}{c}11\\ 3\end{array}\right)=\frac{11!}{3!\cdot 8!}=\frac{8!\cdot 9\cdot 10\cdot 11}{8!\cdot 1\cdot 2\cdot 3}=3\cdot 5\cdot 11=165$  

---

f)

$\left(\begin{array}{c}11\\ 8\end{array}\right)=\frac{11!}{8!\cdot 3!}=\frac{8!\cdot 9\cdot 10\cdot 11}{8!\cdot 1\cdot 2\cdot 3}=3\cdot 5\cdot 11=165$  

---

g)

$\left(\begin{array}{c}12\\ 1\end{array}\right)=\frac{12!}{1!\cdot 11!}=\frac{11!\cdot 12}{1\cdot 11!}=12$  

---

h)

$\left(\begin{array}{c}12\\ 9\end{array}\right)=\frac{12!}{9!\cdot 3!}=\frac{9!\cdot 10\cdot 11\cdot 12}{9!\cdot 1\cdot 2\cdot 3}=5\cdot 11\cdot 4=220$  

---

i)

$\left(\begin{array}{c}100\\ 0\end{array}\right)=\frac{100!}{0!\cdot 100!}=\frac{100!}{1\cdot 100!}=1$  

---

j)

$\left(\begin{array}{c}100\\ 100\end{array}\right)=\frac{100!}{100!\cdot 0!}=\frac{100!}{100!\cdot 1}=1$  

---

k)

$\left(\begin{array}{c}101\\ 99\end{array}\right)=\frac{101!}{99!\cdot 2!}=\frac{99!\cdot 100\cdot 101}{99!\cdot 1\cdot 2}=50\cdot 101=5050$  

---

l)

$\left(\begin{array}{c}102\\ 2\end{array}\right)=\frac{102!}{2!\cdot 100!}=\frac{100!\cdot 101\cdot 102}{1\cdot 2\cdot 100!}=101\cdot 51=5151$