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Teacher Committees

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Fifteen college teachers (A,B,...,O) must serve on a total of twenty committees (1-20), such that:
i) Each teacher is on exactly four committees,
ii) Each committee has three teachers on it,
iii) No two committees have more than one teacher in common.
List (or accurately describe) such a committee structure, or else prove it can't exist.
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A 1 in row i and column j of this matrix indicates


that teacher i is assigned to committee j.
11110000000000000000
00001111000000000000
00000000111100000000
00000000000011110000
00000000000000001111
10001000100010000000
01000100010000000100
00100010000000100010
00010000000100010001
00000001001001001000
10000100001000010000
00001000010000100001
00010000100001000010
00100001000010000100
01000010000100001000
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