Determine with proof the number of ordered triples of sets which have the property (i) and (ii) . So basically this means that all the sets are disjoint.
Not, necessarily. . But that actually makes the problem easier!So basically this means that all the sets are disjoint.
Think of a Venn diagram, see below.
Now the numbers can be placed anyway except into the shaded area. So we are placing "marbles" into 6 "boxes" (because there are 7 sections and we omit the middle section). The formula is:
I really have no idea? I am not a Combinatorics expert .
Perhaps, you can phrase this problem as a Graph Theory problem and then arrive at your answer by computing the adjancency matrix. But I have no idea how to do that.
On a strict reading of this problem as stated, I agree that the answer is .
However, are you sure that you have stated this question correctly?
As stated, the question has several different readings.
I have seen this sort of question many times: “How many ways can {0,1,2,…,8,9} be partitioned into three non-empty, pair-wise disjoint sets?”
Could that be what was meant by this question?