spelling the word Resemblance with E

Solution 1:

Yes. It's resemblance, as your dictionary searches attested.

Unfortunately, in this particular contest there are no rules. Both come from the same sources; some words match the French, some words match the Latin the French is derived from. Often the two match; in other cases they don't.

-ance
From French -ance, from Latin -antia, -entia (from present participial stems -ant-, -ent-).

-ence
From French -ence, from Latin -entia, -antia (from present participial stems -ent-, -ant-). Since the 16th century many inconsistencies have occurred in the use of -ence and -ance.

— Oxford via Lexico

However, in this case, it's actually consistent as the French and its ultimate Latin root has -a-.

resemblance
Middle English from Anglo-Norman French, from the verb resembler (see ʀᴇsᴇᴍʙʟᴇ).

resemble
Middle English from Old French resembler, based on Latin similare (from similis ‘like’).

— Oxford via Lexico

Solution 2:

Apparently it IS a typo since the Answers section of the book has the correct spelling of the word.