A women has 8 close friends.
(a) In how many ways can she invite five of these to dinner? Explain.
(i) 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.
(ii) Repeat part (a), assuming that the eight friends consist of four single people and 2 married couples. If she invites a husband or wife she must invite the spouse. Explain.
(a) This is to select 5 out of 8. So there are C(8,5)=8!/(5!*3!)=56 ways.
(b) In the 56 ways in part (a), we remove the case that the two friends are ...
The solution explains how to use the combination concept.