We present two 1/8 supersymmetric intersecting p-brane solutions of 11
-dimensional supergravity which upon compactification to four dimensio
ns reduce to extremal dyonic black holes with finite area of horizon.
The first solution is a configuration of three intersecting 5-branes w
ith an extra momentum flow along the common string. The second describ
es a system of two 2-branes and two 5-branes. Related (by compactifica
tion and T-duality) solution of type IIB theory corresponds to a compl
etely symmetric configuration of four intersecting 3-branes. We sugges
t methods for counting the BPS degeneracy of three intersecting 5-bran
es which, in the macroscopic limit, reproduce the Bekenstein-Hawking e
ntropy.