1. ## partioning sets...

a set has 5 members.what is the the number ways of partioning it into 2 or more subsets???

2. What things are you given and roughly what knowledge are you supposed to use?

3. all i have is the question.
you should be able to answer it with only high school maths.

4. Originally Posted by earthboy
a set has 5 members.what is the the number ways of partioning it into 2 or more subsets???
Originally Posted by earthboy
all i have is the question.
you should be able to answer it with only high school maths.
I do not consider this to a high school level question.
So I am giving you the technical answer. But I cannot explain to you.
The fifth Bell number is $\mathcal{B}(5)=52$.
That is the number of ways to partition a set of five.
But one of those is the set itself, so it does meet the condition of ‘two or more subsets’.
Thus you answer must be $51$.

5. Originally Posted by earthboy
all i have is the question.
you should be able to answer it with only high school maths.
You could try it using $n_C_r=\frac{n!}{r!(n-r)!}$

You cannot have more than 4 members in a subset.
A subset must contain at least one member.

Therefore you could list the possibilities, then count the number of ways those possibilities can occur.

(a) 4 members in a subset and 1 member in the other subset

For this option, you can count using combinations the number of ways to select 4 from 5 or 1 from 5.

(b) (i) 3 members in a subset and 2 members in another subset

You only need to count the number of ways of selecting 3 from 5 or 2 from 5.
(Selecting any 3 automatically selects the remaining 2 and vice versa)

(b) (ii) 3 members in a subset and 2 subsets containing 1 member

You only need to count the number of ways to choose 3 from 5.

(c) (i) 2 members in a subset and 2 members in another subset
..........(the 5th member automatically makes the 3rd subset of 1)

Select 4 of the 5 and count the number of ways to form 2 groups of 2.
Hence, first count the number of ways to select 4 from 5,
then for each group of 4, count the number of ways to pair one member with one of the other 3.

(c) (ii) 2 members in a subset and the other 3 making single-member subsets

Select 2 from 5 as the remainder automatically form the single-member subsets.

(d) One member per subset