The word "chance" is a noun right? The sentence is "People at a party welcome a chance to make a big impression." And "other" would be a pronoun... right? It says "If you let other people impress you, they will be impressed by your graciousness."
You're right about "chance" being a noun.
"Other" occasionally is used as a pronoun -- but not very often.
Check these definitions to see how "other" is most commonly used. Does that part of speech fit your sentence?
http://dictionary.reference.com/browse/other
Chance can also be used as a verb and an adjective. In this case it IS a noun.
Other in that case would be an adjective.... it describes people.....ie, these people, those people, some people, other people.
Yes, you are correct. In the given sentence, the word "chance" is indeed a noun. It represents the opportunity or possibility for something to happen. In this case, people at a party welcome the opportunity to make a big impression.
Regarding the word "other," you are also correct. In the provided sentence, "other" is being used as a pronoun. It is replacing the noun or noun phrase that has already been mentioned or can be understood from the context. The sentence implies that if you allow other people to impress you, they will in turn be impressed by your graciousness.