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1999 Harvard-MIT Mathematics Tournament
3
1999 HMMT Team #3
1999 HMMT Team #3
Source:
March 8, 2024
combinatorics
Problem Statement
How many non-empty subsets of
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
}
\{1, 2, 3, 4, 5, 6,7,8\}
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
}
have exactly
k
k
k
elements and do not contain the element
k
k
k
for some
k
=
1
,
2
,
.
.
.
,
8
k = 1, 2,...,8
k
=
1
,
2
,
...
,
8
.
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