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by [email protected] » Wed Nov 19, 2008 9:41 am
For a fundraising dinner, a florist is asked to create flower arrangements for 8 tables. Each table can have one of the two types of bouquets available, one with a single type of flower or one with three different types of flowers. If the florist wants to make each table unique, what is the least number of types of flowers he needs?

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by dmateer25 » Wed Nov 19, 2008 10:17 am
Here was my approach to the problem. Please others comment on this.


The minimum amount of flowers you can have is 3.

Bouquet 1 can have flowers: 1, 2, or 3

Bouquet 2 would have flowers: 1, 2, and 3


So in this case you would have:

Table 1…..1
Table 2…..2
Table 3…..3
Table 4…..123
Table 5
Table 6
Table 7
Table 8

However, you run out of unique arrangements after 4 tables.

So let’s try 4 types of flowers

Bouquet 1 can have flowers: 1, 2, 3, or 4

Bouquet 2 cab have flowers: 123, 124, 134, and 234

To get bouquet 2 you could also do:
4c3 = 4!/3!(4-3)! = 4

So in this case you would have:

Table 1…..1
Table 2…..2
Table 3…..3
Table 4…..4
Table 5….123
Table 6….124
Table 7 ….134
Table 8…..234


So you need 4 types of flowers to make 8 unique arrangements.
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