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International Contests
Austrian-Polish
1995 Austrian-Polish Competition
6
6
Part of
1995 Austrian-Polish Competition
Problems
(1)
E_i \cap E_j \ne\varnothing, 4mountain trips for n Alpine Club's members
Source: Austrian - Polish 1995 APMC
5/3/2020
The Alpine Club organizes four mountain trips for its
n
n
n
members. Let
E
1
,
E
2
,
E
3
,
E
4
E_1, E_2, E_3, E_4
E
1
,
E
2
,
E
3
,
E
4
be the teams participating in these trips. In how many ways can these teams be formed so as to satisfy
E
1
∩
E
2
≠
∅
E_1 \cap E_2 \ne\varnothing
E
1
∩
E
2
=
∅
,
E
2
∩
E
3
≠
∅
E_2 \cap E_3 \ne\varnothing
E
2
∩
E
3
=
∅
,
E
3
∩
E
4
≠
∅
E_3 \cap E_4 \ne\varnothing
E
3
∩
E
4
=
∅
?
combinatorics