For those who, for one reason or another, can't live in their own island paradise, the slide show presentation entitled "Montgomery County: A County of Choice" makes the choice quite clear. There is always Montgomery.

The county government and local business leaders plan to use the slides to attract new business to Montgomery. And what one sees in the presentation are pictures of smiling families in spacious backyards, elegant old homes in Chevy Chase and Gaithersburg, a typical homestead in Potomac with three acres of land and a white rail fence, specialty shops and famous-name clothing stores.

There were all sorts of tantalizing facts about the county, too, that made you feel that if you don't now live in Montgomery, well, you ought to.

For example, half the adults in the county, the narrator tells us, are college graduates. And 70 percent of their children go on the college.

One third of the area's doctors, lawyers, chemists, engineers and dentists already live in Montgomery.

The county has 20,000 acres of park land, more than 500 public and private tennis courts, 26 golf courses and dozens of public and private swimming pools, not to mention its polo clubs and old established hunt club.

In addition, Montgomery has "the highest concentration of country clubs" in the Washington area.

The slide show was presented to county officials and reporters for the first time last Friday. That same afternoon another Montgomery Conty news story developed - one that provided a rare glimpse of another side of the county.

It had to do with 17-year-old Andy Hart who lives in a subsidized housing project called Emory Grove Village, nestled away on the outskirts of Gaithersbury. With her late husband's Social Security benefits. Hart's mother supports herself and the three of her nine children who live at home. And Hart, who was failing at Magruder High School, was working nights as a janitor at the Bechtel Corporation. He was looking for a better job, one of his brothers said, to contribute toward the support of his one-month-old son, who now lives with his 15-year-old girl friend.

Hart had been arrested that morning with a man named Victor Saadeh. Police said Saadeh paid Hart a total of $120 to kill Saadeh's wife's boyfriend.

Hart and Saadeh have been charged with murder.

Andy Hart's story is as much a part of Montgomery County as I. Magnin's and the Potomac Hunt Club. Yet, he belongs to a side of Montgomery that is rarely investigated. It's the side of Montgomery that just doesn't fit its image as the aristocrat of the Washington suburbs.

Of course, it's more interesting to write about those aspects of Montgomery that seem to have sprung from the pages of an F. Scott Fitzgerald work: its country clubs, its wide estates, its chic shops, its wealthy and educated population, its bored and troubled teen-agers who turn to crime or drugs.

But the longer you look at Montgomery, the clearer it becomes that there is an underside to every aspect of its ideal image.

True, there are $200,000 homes in Potomac. But in Silver Spring, which has one of the Washington area's largest concentration of Hispanic immigrant families, six- and seven-member families live in three-room apartments.

And often in those $200,000 homes, there are two or three rooms devoid of furniture.

It is true, too, that the county boasts a larger percentage of doctors per capita than any other area jurisdiction and an average household income of $28,000. Yet its main health problems, according to a recent, detailed report by the Health Systems Planning Agency, are alcoholism and poor nutrition.

Despite these contradictions, the view of Montgomery offered in the slide show - that of a wealthy, well-serviced, well-education community - remains intact. It survives because people want it to. And because the image, after all, is as much a part of Montgomery as the contradictions.