Eight Cabinet officers and four officials of Cabinet rank were sworn in yesterday in what President Carter called "the first official and completely open ceremony" of his administration.

The President attempted to tone down the pomp of the circumstance, drawing applause as he said, "We decided to forgo the 'Ruffles and Flourishes' and 'Hail to the Cheif.'"

He also noted dryly that he would have liked to have sworn in all 11 regular officers of his Cabinet yesterday, but the Senate was a bit reluctant to go along with all of his choices. "I've always heard about the advise and consent role of the Congress," he said. "but so far, they've been a little stronger on the advice than on the consent."

The three members of Carter's chosen Cabinet who did not participate in yesterday's ceremony are Attorney General-designate Griffin B. Bell, Labor Secretary-designate F. Ray Marshall and Joseph A. Califano Jr., Secretary-designate of the Department of Health, Education and Welfare.

Though all three have faced opposition to their nominations - with Bell drawing most of the criticism - they are expected to be confirmed by the Senate this week.

To those who were sworn in yesterday, vowed that there would be no White House meddling in their offices.

"There will never be an instance, while I am President, when the members of the White House staff dominate or actually take a superior position to members of our Cabinet," he said.

The Presidnet added: "When any directive is relayed from the White House to the members of teh Cabinet, it will indeed come directly from me."

"I believe in a Cabinet government," Carter said. "And although the major decisions will be made by me, as President, which is my constitutional prerogative and responsibility, the secretaries Cabinet officers) will run their own departments."

Carter said that arrangement will put a "heavy responsibility" on him because "it's a departure from previous policy." But he said it will also put a heavy responsibility on the Cabinet members.

"This is the way it ought to be," Carter said. "And because I recognize this challenge to them, I was particularly careful with my selections . . . I feel quite confident that I can do a good job as President because of the superb qualities of those who will help me."

Cabinet officials sworn in yesterday by Chief Justice Warren E. Burger were Secretary of State Cyrus R. Vance, Treasury Secretary W. Michael Blumenthal, Defense Secretary Harold Brown, Interior Secretary Cecil D. Andrus, Agriculture Secretary Bob Bergland, Commerce Secretary Juanita M. Kreps; Patricia Roberts Harris, Secretary of the Department of Housing and Urban Development, and Transportation Secretary Brock Adams.

Officials of Cabinet rank who took their oaths yesterday were Thomas B! (Bert) Lance, director of the Office of Management and Budget; James R. Sclesinger, energy chief; Charles L. Schultze, chairman of the Council of Economic Advisers, and Zbigniew Brzezinski, national security adviser.

Carter introduced the new officers individually, using phrases like "one of the closest friends I have in the world" (Lance), an adviser "whom I've already come to love" (for Kreps), and "the one I feel the deepest sense of mutual sympathy with" (Bergland).

The new officers stood on the podium with their spouses behind the black and white name plates on the floor. There also was a plate for the President - marked "The President" - next to the presidential rostrum. The "completely open ceremony" ended with a reception that was closed to the press. And the full-dress Marine Corps band that had been asked to bypass "Ruffles and Flourishes" and "Hail to the Chief" could be heard entertaining the guests with "Georgia on My Mind."