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Q: i want to choose 4 people out of 4 couples. i want a group with at least 1 couple. | |
4 couples: | |
ab | |
cd | |
ef | |
gh | |
> > > selecting among the four couples is: | |
> > > (4 choose 1) = 4 | |
> > > This part of your work was the AHA! for me to see the formal answer: | |
non-couples: | |
6:a(c,d,e,f,g,h) | |
6:b(c,d,e,f,g,h) | |
4:c(e,f,g,h) | |
4:d(e,f,g,h) | |
2:e(g,h) | |
2:f(g,h) | |
-- | |
24 | |
pre-selecting one couple reduces # of selectable non-couples to 12. | |
> > > 12 is the number of non-couples after pre-selection: | |
> > > (3 choose 2) * (2 choose 1) * (2 choose 1) = 12 | |
> > > choose two of remaining couples, and from each couple, choose 1 person | |
couple(couple): | |
3:ab(cd,ef,gh) | |
2:cd(ef,gh) | |
1:ef(gh) | |
- | |
6 | |
> > > this is the two couple scenario: | |
> > > (4 choose 2) = 6 | |
for each couple: | |
couple(12 non-couples + remaining selectable couples) | |
15:ab(12 + 3) | |
14:cd(12 + 2) | |
13:ef(12 + 1) | |
12:gh(12) | |
-- | |
54 | |
== | |
> > > the possible ways to pre-select is (4 choose 1) = 4, and thus | |
> > > the number of ways to pre-select a couple, and then choose a non-couple is: | |
> > > 4 * 12 = 48 | |
> > > And then add that to the ways to select 2 couples: | |
> > > 6 + 48 = 54 |
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