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Combinations: woman invite five of her nine close friends to dinner

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A woman has 9 close friends.

(a) In how many ways can she invite five of these to dinner? Explain/show work.

(b) Repeat part (a) with the added stipulation that two of her friends do not like each other so that if she invites one of them she cannot invite the other. Explain/show work.

(c) Repeat part (a), assuming that the nine friends consist of five single people and 2 married couples. If she invites a husband or wife she must invite the spouse. Explain/show work.

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Solution Summary

This solution discusses how the combinations are determined in 132 words. Calculations and answers are provided.

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(a) This is to select 5 out of 9. So there are C(9,5)=9!/(5!*4!)=126 ways.
(b) In the 126 ways in part (a), we remove the case that the two friends are invited together. In this ...

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