What does Charlotte's comment, "Happiness in marriage is entirely a matter of chance," tell us about her?
Charlotte Lucas's marriage to Mr. Collins is more realistic and a more accurate representation of what marriage was like for women in 19th century England. Charlotte's marriage to Mr. Collins is an arrangement of convenience, he needed a suitable wife, she needed a husband, love is not part of the equation.
In fact Charlotte tells Elizabeth Bennet when she visits that the less she sees of Mr. Collins the better. Therefore, the marriage is a formality that she entered into to change her status from single to married. She did not want to be a spinster, so she accepted Collin's proposal even though she does not love him, she tolerates him. She has a comfortable home, appears content, happiness is not necessary, she is satisfied.
What it tells us about Charlotte Lucas is that she is rational and reasonable and does not believe in the idea of being in love the way that Lizzie Bennet does.
"Charlotte Lucas is Elizabeth Bennet's best friend. She distresses Elizabeth by deciding to marry William Collins, Mr. Bennet's nephew, out of interest in his estate. Up until this point Elizabeth had respected Charlotte's sensibility, but her decision to marry Mr. Collins lost her much of Elizabeth's respect."
Charlotte marries Mr. Collins, after he is rejected by Lizzie, she does not hesitate to accept his proposal. She is logical and realistic regarding her future as a single woman, she needs a home of her own and the only way to get it is by marrying someone who could provide for your future.
Jane Austen's fairy tale marriages of Lizzie Bennet and Jane Bennet to men they love and who are very rich are just that a fantasy. The idea the young women in 19th century Britain dreamed about, but rarely happened.
When Charlotte says that she is acknowledging that in society marriage I not done for love, as Elizabeth would like it, but rather for spousal security and funding. Being in love in a marriage for Charlotte is like rolling dice. If it happens it purely out of luck. Also the older Charlotte gets the less likely she is to find a suitor who is willing to marry her and thus she will continue to be a burden to the family. So For Charlotte marrying for love is not something she can do, especially with status. With any man looking to marry her Charlotte will have no choice but to marry him in fear of being a burden to the family as well which she does with Elizabeth's cousin. Charlotte's statement just confirms her reality of her situation and how love is not guaranteed in marriage.
I think it also shows a contrast between her and Elizabeth. I agree that it is more realistic. Austen uses her to show that a good marriage can only come from love, like lizzie and Darcy.