COMP 2711 Ex 6

1

a

$$C_5^{10}=252$$

b

The complement of contain at least one element in ${\mathbb{Z}}_3$ is contain no element in ${\mathbb{Z}}_3$

$$C_5^{10}-C_5^7=231$$

c

$$\begin{array}{rl}& \text{Odd numbers in }{\mathbb{Z}}_{10}=\left\{1,3,5,7,9\right\}\\ & \text{Even numbers in }{\mathbb{Z}}_{10}=\left\{0,2,4,6,8\right\}\end{array}$$

Choose 2 odd numbers and 3 even numbers

$$C_2^5{C}_3^5=100$$