Probability and random variable
Consider the sets $A_1, A_2, A_3 \dots A_m$ each a subset of size $k$ of $\{1,2,3, \dots , n\}$. If in a 2-colouring of $\{1,2,3, \dots , n\}$ no set $A_i$ is monochromatic, then show that $ m < 2^{k-1}$.
Consider the sets $A_1, A_2, A_3 \dots A_m$ each a subset of size $k$ of $\{1,2,3, \dots , n\}$. If in a 2-colouring of $\{1,2,3, \dots , n\}$ no set $A_i$ is monoch...