Ralph decides that he, Jack, and Simon should go and search the land to make sure that it is indeed an island. This is signifincant because Ralph is the newly selected leader while Jack has been a leader of half of the boys already. These two choices were easy for Ralph. But the third choice seems to be a random selection. Simon is described at this moment of selection like this:
...he was a skinny, vivid little boy, with a glance coming up from under a hut of straight hair that hung down, black and coarse.
Simon is a quiet character and a reason why he may be part of this group will be revealed later, by chapter 9. Piggy wanted to join the boys and be a part of the expedition, but Ralph wouldn't let him come along.
Ralph, Jack, and Simon are the three boys who go out and explore the surroundings in order to determine if they are on an island or not. Their exploration occurs in chapter 1 right after Ralph is chosen to be chief. Jack is obviously disappointed at not being selected chief, and Ralph is smart enough to realize this fact. As a way to ease Jack's disappointment, Ralph tells Jack that he can be in charge of the hunters.
“Jack’s in charge of the choir. They can be—what do you want them to be?”
Jack and the other choir boys then take off their "togs," and Ralph notices that Jack's legs are sticky with sweat. Jack explains that he was trying to reach higher elevation in order to figure out if they crashed on an island. Ralph agrees that figuring out if they are on an island or not is a good idea. He correctly understands that if they are on an island, rescue will not be coming as soon.
"If this isn’t an island we might be rescued straight away. So we’ve got to decide if this is an island."
Ralph also decides that it isn't smart for every single boy to go on the scouting trip. Ralph decides that three boys should go and everybody else should stay behind and wait. Ralph volunteers himself and Jack. He then looks around and sees a bunch of eager faces, and Ralph decides that Simon will be the third boy.
"Everybody must stay round here and wait and not go away. Three of us—if we take more we’d get all mixed, and lose each other—three of us will go on an expedition and find out. I’ll go, and Jack, and, and....”
He looked round the circle of eager faces. There was no lack of boys to choose from.
Piggy is unhappy with not being chosen, and he attempts to tag along, but Ralph and Simon firmly tell Piggy that he isn't welcome.
Ralph turned to him. “You’re no good on a job like this.”
“All the same—”
“We don’t want you,” said Jack, flatly. “Three’s enough.”