How many rays are originating from O?
 

A part of the line which has a fixed starting point but no endpoint is called a Ray.

So, in the figure,

we can see, there are four rays originating from O which are $\overrightarrow{\mathrm{OC}}, \overrightarrow{\mathrm{OA}}, \overrightarrow{\mathrm{OD}}, \mathrm{and} \overrightarrow{\mathrm{OE}}$.