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Word problem

I've attached the file. I need to know if I'm going in the right direction (in the red font), if not could you explain?

(See attached file for full problem description)

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A person has 14 close friends.

(a) How many ways can she invite 8 of her 14 close friends to a holiday get-together. Explain.

(b) Suppose that out of her 14 friends 8 are women and 6 are men.
(i) How many groups of 8 people can she invite that contain 5 women and 3 men? Explain.

(ii) How many groups of 8 people can she invite that contain at least 1 man? Explain.

(iii) How many groups of 8 people can be formed that contain at most 5 women? Explain.
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(See attached file for full problem description)

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