We present two 1/8 supersymmetric intersecting p-brane solutions of
11-dimensional supergravity which upon compactification to four dimensions
reduce to extremal dyonic black holes with finite area of horizon. The first
solution is a configuration of three intersecting 5-branes with an extra
momentum flow along the common string. The second describes a system of two
2-branes and two 5-branes. Related (by compactification and T-duality) solution
of type IIB theory corresponds to a completely symmetric configuration of four
intersecting 3-branes. We suggest methods for counting the BPS degeneracy of
three intersecting 5-branes which, in the macroscopic limit, reproduce the
Bekenstein-Hawking entropy.Comment: 15 pages, harvmac; a reference added (the version to appear in
Nulcear Physics B