How we cite our quotes: (Chapter.Paragraph)
Quote #4
"Thank you," said Floyd with a smile, wondering why stewardesses always had to sound like robot tour guides. (7.24)
Even in the future, the stewardesses are all women. Floyd wonders why she has to sound like a robot—but the answer is that she, like all the women in the book, doesn't get to be a real person, she's just window-dressing.
Quote #5
…she came from Bali, and had carried beyond the atmosphere some of the grace and mystery of that still largely unspoiled island. (9.43)
One of the stewardesses on the moon-flight is from Bali, and she does a dance for Floyd. Bali is presented as primitive, and the woman is linked to that primitiveness. Floyd is the manly dude flying into space, contrasted with the sensual, exotic woman doing her sexy dance for his pleasure and entertainment.
Quote #6
Floyd found himself back in the familiar environment of typewriters, office computer, girl assistants, wall charts, and ringing telephones. (10.21)
Again, "girl assistants" are part of the furniture, like "wall charts" or "ringing telephones". Clarke's future is mired in the gender assumptions of 1968. Other science fiction of the era (like Ursula K. Le Guin's Left Hand of Darkness) imagined gender reconstructed and rejiggered. Not Clarke though; for him, it's all still about the girl assistants.