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Word problems and counting techniques

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A person has 14 close friends.

(a) Suppose that two of her friends (of the 14 of either gender) do not like each other. If one of the two is invited, the other will not come to the party. How many ways are there to invite 8 people to the party. Explain.

(b) Suppose that two of her friends are a couple. She cannot invite one of the 2 without inviting the other. How many ways are there to invite 8 people to the party. Explain.

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Solution Summary

This shows how to solve a word problem involving counting techniques.

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(a) To invite 8 people with respect to the condition, there are 2 cases:
case 1: Select any 8 out of 12 people without the two friends. There are ...

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