A program designed to train and find permanent jobs for 920 unemployed Washington residents was launched yesterday by a new local group, formed as part of a nationwide partnership between business and government.

The D.C. Private Industry Council (PIC) said it has selected 10 firms and organizations to provide training and job placement services over the next five months under a $1.4 million grant from the U.S. Department of Labor. Individual firms will train specific groups of unemployed persons such as former prisoners, youth and economincally disadvantaged women.

Although the training will be subsidized by the government, the eventual jobs will be provided by private industries.

Mayor Marion Barry, speaking at a news conference, said the industry council has forced on training for various types of service jobs in which there is a shortage of qualified workers. "This kind of specificity and targeting is the key, I believe, to . . . success," Barry said.

Kent T. Cushenberry, chairman of the D.C. Private Industry Council, said all program participants must be registered with the D.C. Department of Employment Services under Title Seven of the Comprehensive Employment and Training Act (CETA). Trainees will earn the federal minimum wage of $3.10 an hour.

The creation of the councils to oversee such job programs in major cities and large urbanized counties was authorized by a federal law last year. The D.C. council, created by Barry in an executive order, is composed of 33 people representing businesses, community organizations, organized labor, educational institutions, and the city government. Organizations chosen to provide the training, their type of jobs and the number of trainees are:

Liberation of Ex-Offenders Through Employment Opportunity, counseling and job placement, 140; Opportunities Industrialization Center, printing, clerk-typists and telecommunications technology, 115; Wider Opportunities for Women, air conditioning, heating and refrigeration, auto mechanics and pre-apprenticeship training, 57; ITT Education and Training Systems, telephone installation, 40.

Also, Public Art Works, Inc., artists and muralists, 20; Greenfield Laborers & Construction Industries Institute, construction, 120; Action Radiator Company, auto air conditioning, 40; Association Personnel Inc., association management training and clerks, 328; Research Information Systems & Evaluation Inc., word processing, 20; and Washington Urban League, word processing, 40.