TGC wrote:
How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?
A.16
B.27
C.31
D.32
E.64
The solution offered counted it differently.
So I just want to clear it up whether I am also thinking in the right direction.
Number of subset
Since we have 5 digits other than 0, we can take any numbers from the set of 5 to make a subset. Also it is a matter of selection and not arrangement.So we will consider combinations.
5c1+5c2+5c3+5c4+5c5=31
And one set is the NULL set having no elements in it so
31+1=32
Please confirm my reasoning of NULL set.
Rgds,
TGC!
That's correct. Check here:
http://gmatclub.com/forum/fresh-meat-15 ... l#p1243696Another solution is here:
http://gmatclub.com/forum/fresh-meat-15 ... l#p1215329Consider the set without 0: {1, 2, 3, 4, 5}. Each out of 5 elements of the set {1, 2, 3, 4, 5} has TWO options: either to be included in the subset or not, so total number of subsets of this set is 2^5=32. Now, each such set will be a subset of {0, 1, 2, 3, 4, 5} and won't include 0.
Answer: D.
Hope it helps.
I can understand the approach. But how do you apply similar approach for the following question?
.
Set S contains 7 different letters. How many subsets of set S, including an empty set, contain at most 3 letters?
A. 29
B. 56
C. 57
D. 63
E. 64