# Heavy exercise: No. of subsets of a set

Iorgu
Visitor
2016-01-12 03:17:28
#1
Hi,

I need to know this problem for an exam.
Let's find out n (natural number) for which the set {1, 2, 3, ... , n} has exactly 120 subsets , 2 element subsets.

## RE: Heavy exercise: No. of subsets of a set

IanTeach
Visitor
2016-01-12 05:34:42
#2

The number of the a elements subsets of a set with n elements is given by combinations. So though, we got:

## RE: Heavy exercise: No. of subsets of a set

IanTeach
Visitor
2016-01-12 05:36:21
#3

$C_{n}^{2} = \frac{n!}{2!\cdot (n-2)!} = \frac{(n-1)n}{1\cdot 2}=\frac{(n-1)n}{2}$

So,

## RE: Heavy exercise: No. of subsets of a set

IanTeach
Visitor
2016-01-12 05:37:17
#4

$\frac{(n-1)n}{2}=120$

$n^{2}-n-240=0$

You have to solve this eqution n.