In a victory for President Carter the Senate Governmental Affairs Committee voted unanimously yesterday to create a new Department of Education with about 24,000 employes and an annual budget of $18 billion.

His argument represents a fresh challenge to the missile deployment scheme gaining momentum within the government as Carter administration officials look for ways to assure the Senate and the public that signing a new arms control agreement with the Soviets is an acceptable risk.

The shell-game concept calls for digging 20 holes for one missile. The missile, complete with launched, would be trucked from hole to hole secretly, perhaps darkness, so that the Soviets could never be sure which underground silo held a missile.

If Soviets did not know which of 20 silos had the missile, backers of the scheme argue, they would have to use up at least 20 warheads to cover the field hiding the single missile.

The bill's chief sponsor, committee chairman Abraham A. Ribicoff (D-Conn.), smiled broadly during the 14-to-0 vote but warned that only "a few short months" remain to push the bill through the Senate and House before the 95th Congress adjourns.

When the measure goes to the Senate floor, American Indian and agricultural interests will try to strip the new department of its control over Indian education programs and $3 billion worth of school-lunch, school-breakfast and related child-nutrition programs.

Yesterday, spokesman for three different organizations of American Indians said that they want Indian education programs to stay in the Interior Department's Bureau of Indian Affairs.

Meanwhile, Sen. Charles H. Percy (R-Ill.), who voted for the bill in committee, said he would seek floor action to keep the child-feeding programs in the Agriculture Department instead of shifting them to the Education Department. Last week, the committee voted 8 to 7 to put the feeding programs in the Education Department.

In the House, where subcommittee hearings have started, the bill also faces a difficult path.

As approved by the Senate Governmental Affairs Committee, the new department would be made up of dozens of programs shifted from existing Cabinet departments, chiefly the Department of Health, Education and Welfare.

The heart of the new agency would be the entire existing education division of HEW - $12.9 billion a year in programs and 3,600 persons. This includes elementary and secondary education programs, impact aid, college aid, student assistance, vocational education, library aid, bilingual education and the National Institute of Education.

Also to be included: HEW's vocational rehabilitation programs ($912 million): The Defense Department's overseas schools for dependents of service personnel ($350 million and 10,000 teachers and administrators); the BIA Indian schools ($271 million and 6,550 employes); child nutrition ($3 billion, of which $560 million would be used by the Agriculture Department for program food purchases); HEW's civil rights personnel for education (12,000 persons); and various college housing and education construction loans.

The new department also would have supervisory power over Howard University, Gallaudet College, the American Printing House for the Blind and the National Technical School for the Deaf.

The bill came out essentially as Carter sought with two exceptions: it would leave Head Start in HEW instead of shifting it to the Education Department, and it would move vocational rehabilitation to the new department (the president had wanted that left in HEW).

The bill would leave veterans' educational programs in the Veterans' Administration and would leave the National Foundations on the Arts and Humanities, the Smithsonian and the National Science Foundation independent, although a small number of NSF science training programs ($56 million) would be shifted to the Education Department.

Before the VOTE, Sen. William V. Roth (R-Del.) offered an antibusing amendment to the charter of the new department but withdrew it after Ribicoff, Sen. Sam Nunn (D-Ga.) and Sen. Lawton Chiles (D-Fla.) argued that its addition might threaten passage of the whole measure. "I can count," said Roth, mentally tabulating the probable votes. He said he might raise the amendment on the floor.