Question

Five men, Adam, Bill, Clint, Derek and Ed, are broken into two groups, one with two men and one with three. Different orders within each group are not considered distinct. One possible outcome is that Adam and Derek are grouped together and Bill, Clint and Ed are grouped together. We will denote this outcome by (AD, BCE

). Using this notation, give the sample space for this experiment.

NOTE:

The act of breaking a set up into smaller sets is called partitioning the set. Note

that each of the smaller sets is a subset of the original set,

no object is in more than one of the subsets,

the union of all of the subsets is the original set.

Answer 1

The sample space is as follows

With Adam in group 1 with 2 people, we have

(1) (AB, DCE)

(2) (AC, BDE)

(3) (AD, CBE)

(4) (AE, BCD)

With Bill in first group...Not considering with Adam, as the same has been denoted in (1).

(5) (BC, ADE)

(6) (BD, ACE)

(7) (BE, ACE)

With Clint in first group...Not considering with Adam and Bill, as the same has been denoted in (2) and (5).

(8) (CD, ABE)

(9) (CE, ABD)

With Derek in first group...Not considering with Adam, Bill and Clint, as the same has been denoted in (3), (6) and (8).

(10) (DE, ABC)