Indefinite article optional?

Hi. I think I have seen very many sentences in Google Books with the phrase "have opportunity to do" and "have responsibility to" without the indefinite article "a" in front of the words "opportunity" and "responsibility." I have a rough feeling that possibly in most cases having the indefinite article "a" in front of the words "opportunity" and "responsibility" is optional. Is my feeling trustworthy? Is it correct?