In the lecture, Example $10\mathrm{.}03$ tells us that there are three different ways to choose a substring y for the language

: first, contains only a$\text{'}$s; second, contains only b$\text{'}$s; third, contains both a$\text{'}$s and b$\text{'}$s$.$ Given a language

where

$,$ using the same approach as in Example $10\mathrm{.}03,$ how many different ways are there to choose the substring y when applying the pumping lemma? $($Your answer must be a whole number, such as $10)$