A hint to get started
Find one mode or two exactly tied modes
In a village with a large population, 80% of inhabitants have a particular eye disorder. (i) If 12 people wait to see the nurse, find the most likely number with the disorder. (ii) If 19 people wait, find the most likely number.
CJC · Lecture · Example 10
Search for the largest mass, rather than rounding the expectation.
Retain both maxima when their exact probability ratio is 1.