Correct spelling, explanation: admission is the word of Latin origin, which appeared in the times of Middle English. Grammatically, it is a noun that is widely used in both written and spoken language. When it comes to spelling it is worth noticing that admission features a single -d letter.

Definition of admission:
noun – agreeing, often reluctantly, that something is true,
He left the room without saying a single word, which for me was an admission of guilt.
noun – the charge for entering a place,
They charge $10 for admission to the club.
noun – permission to enter some place,
Admission to the party is only for the invited people.

Collocations with admission:
Some common collocations include: free admission, apply for admission, admission of defeat
The city council is the sponsor of the event so there is free admission.
Once he passes his exams at high school, he’s going to apply for admission to college.
Leaving the pitch in the middle of the game was his admission of defeat.

Incorrect spelling, explanation: a common mistake in the word admission is to double the letter -d, which results in an incorrect form addmission. The mistake probably comes from the fact that many users of English wrongly assume that admission is the combination of two words: add and mission.