The indefinite articles a and an are used to modify singular nouns. When using a plural noun, these two articles are unnecessary. Plural nouns can take either a definite article or no article at all.
The definite article is the word the. It precedes a noun when something specific (i.e., definite) is being referred to.
Indefinite articles, on the other hand, are used before nouns that are nonspecific within their class.
We do not know from this statement who specifically this lady is. We only know generally that the person is a lady.
Plural nouns can be used with the definite article or no article at all; to use an indefinite article would be incorrect.
It is also unnecessary to use an indefinite article if there is an adjective in front of a plural noun.
A is not necessary in this sentence and should be removed. However, if you want to refer to the specific quantity of options, the sentence can be rephrased to use the definite article the with a plural noun:
You can explore more by reading Articles: Grammar Rules and Plural Nouns: Rules and Examples.