cbaum wrote:We are left with 6, and these represent people who have been counted 3 times - once for each group. We want to leave one instant of these employees, so these 6 employees represent two instances of 3 employees that work in all 3 restaurants.
Hi, could someone please explain why/how we get from 6 to 3? I'm not quite clear on the explanation above.
Now, that is a good question.
Think of each number of people in a group as a list of names in an excel spreadhsheet. We start by adding three lists: 19 + 18 + 12 = 49. We now have a spreadsheet with 49 names, but some of these names are duplicates:
The 4 that are members of 2 groups (doesn't matter which ones) appear on the list twice - for example, john was added twice, once as part of the 19 people in the buffet, another time as part of the 12 people in the snack bar.
And there is an unknown quantity of names that appear three times - once for each of the three restaurants they work in. Sally is a busybee that works at all three restaurants, so when we added the original lists together, we created three "sallys" who are actually the same person.
You know that there are only 39 employees, and your job is to clear up this mess - leave the list with a final 39 names, every name counted only once. What do you do?
The 4 that were counted twice (John), you only want to count once - so you subtract one instance of their name: subtract 4. Great, now we only have 49-4=45 names on the list - we still have 6 names extra.
The others that were counted THREE times (Sally), you still want to only count once - so you have to strike out TWO instances of each of the triples. So these 6 extra actually count for only 3 people, each appearing twice: two Sallys, two Thelmas, two Louises that we want to take out and leave the last instance of their names in the list of 39.
