It's amusing, in a discouraging way, how broadcast brass can predict long life and prosperity for network television on one hand and then cough up a feeble burble of frivolity like "The Facts of Life" on the other, NBC's new comedy series, premiering tonight at 8:30 on Channel 4, amounts to, if not a suicide note, at least a network's poison-pen letter to itself -- veritable ballyhoo for doomsday.

Although NBC has ordered only four episodes from TAT Communications, production will continue if the show scores good ratings. This speaks ill of network TV and the way it works; although the program is worthless and barren, it might slink into the survivor bracket since it follows, and was spun off, NBC's one comedy hit, "Diff-rent Strokes."

The premise has Charlotte Rae, the jolly housekeeper of "Strokes" -- and a kind of poor man's Shirley Booth -- taking on a temporary assignment as housemother at a girls' school located somewhere beyond the boundaries of belief. In the premiere, to hold onto the "Strokes" viewers, young Gary Coleman and costars Conrad Bain and Todd Bridges make quick and superfluous guest appearances. Coleman's ebullient mugging as Arnold proves the funniest thing on "Facts" just as it is the entire raison d'etre of "Strokes."

When one of the girls in the school coos "Arnold, you're so darling" and tries to pinch his pinchable cheeks, Coleman sputters, "Give me a break, please!" Later he laments, "it's a curse to be darling."

Otherwise the high point of Brad Rider's script is an exchange between a teacher and a student: "Some of you are about to burgeon into womanhood," the teacher says, and the student replies, "I thought all of us were burgeons." It gets worse, but it doesn't get any better.

To excuse the formula banality, a formula moral lesson is interpolated into the storyline, but the effect is more unsettling than uplifting. A young tomboy type (touchingly played by Julie Ann Haddock) is taunted by a prematurely voluptuous boy-killer (Lisa Whelchel) with the accusation that she has lesbian tendencies.

This little twist on "The Children's Hour" seems an ill-advised theme for a show in territory still widely regarded as the family hour, and it is resolved in a sappily pat way. The girls learn it is okay to hug one another after all, so there's a big clincho between the adversaries at the fadeout. It's all lamely and depressingly predictable as the decline of the dollar. The decline of the networks is predictable too, but hardly depressing considering the "The Facts of Life" and the machinery that produced it.