The Washington Post Co. announced yesterday that it has acquired an 18 percent interest in a partnership of all applicants for a cellular radio license in the Detroit area.

A Post subsidiary, Post Cellular Telecommunications Michigan Inc., will join in seeking the license to provide expanded mobile telephone service with American Mobile Communications of Michigan and Ohio, Celcom Communications Corp. of Michigan Inc., Cellular Mobile Systems of Michigan Inc. and Unity Telecommunications Systems Inc.

The price of the Post's share of the partnership was not disclosed.

Once the license is approved by the Federal Communications Commission, construction of the first portion of the system is expected to be completed in 12 to 15 months, the company said.

The Post also announced yesterday the completion of its previously reported acquisition of 50 percent of SportsChannel Associates and approximately 25 percent of New England SportsChannel. The Post acquired its interest from Cable Program Enterprises for an undisclosed price.

Both organizations offer extensive subscription and cable sports programming in major markets.

SportsChannel, in the New York area, carries many New York Mets and Yankees baseball games, New York Islanders and New Jersey Devils hockey, New Jersey Nets basketball, and horse racing. The service has more than 380,000 cable and subscription clients, the Post said.

New England SportsChannel carries Boston Celtics basketball and Hartford Whalers hockey, and offers SportsChannel's New York and New Jersey games in most of New England.