“Yes. Not Good Humor, but a truck of that size. That’s exactly what I meant.”
“We carry ’em.”
“What was that? I’m sorry, I’m a little deaf.”
“I said we carry ’em. Ice-cream trucks.”
“Do I need a ticket in advance, or can I buy it on the ferry?”
“You buy it on the ferry.”
“Would you mind looking at this ferry schedule, please?” the deaf man said, and he shoved the schedule under the barred window. The ticket seller did not look up. His eyes shifted toward the schedule, but he continued counting, and he would not look up at the deaf man.
“What about it?”
“It says it’s effective April 13. That’s next Monday.”
“That’s right. What about it? We still got some old schedules over there, if you want them.”
“No, no, this is just what I want. But will these arrivals and departures be in effect for a while?”
“Absolutely. Don’t put out a new schedule until June sometime. And even that’ll be the same, actually, except it makes people feel better when they see new dates on a timetable.”
“Then these times will be in effect throughout April and May, is that right?”
“June, too,” the ticket seller said. “AndJuly, for that matter.And August. Schedule don’t change again until we go off daylight-saving time. That’s in September sometime.”
“I see, thank you. And I can buy a ticket for the truck after I have boarded the ferry with it, is that also correct?”
“Yes, that’s right.”
“Should I get here very far in advance, or can you usually accommodate all the vehicles that want passage?”
“We got room for twenty-five cars. Seldom get more’n a dozen. Plenty of room aboard the old tub. Not many people want to go to Majesta. Sure, it’s nice and quiet there, but it ain’t exactly anybody’s idea of city life, if you know what I mean.”
“Well, thank you very much,” the deaf man said. “What time does the next ferry leave?”
The ticket seller did not stop counting, nor did he look up at the clock or down at his wrist watch. He simply said, “Eleven o’clock.”
“Thank you,” the deaf man said. He walked away from the window, nodded pleasantly at a uniformed cop standing near the newspaper stand, and strode rapidly to where Rafe was sitting on the bench. He sat beside him unobtrusively.
“I’ll be going over to Majesta,” he said. “You have some phone calls to make, don’t you?”
“Yes, I do,” Rafe said, nodding. The sight of the uniformed cop made him somewhat anxious. He did not like policemen. He had spent five years in prison because of policemen.
“I just checked the schedule,” the deaf man told him. “We’ll plan on catching the 5:45P.M . boat on the evening of the caper. The one after that is at 6:05. That gives us a twenty-minute leeway, should anything go wrong.”
“Do you think anything will go wrong?” Rafe asked. He was a tall thin man with a mild manner, a manner accentuated by the gold-rimmed eyeglasses and sandy-blond hair.
“No,” the deaf man said confidently. “Nothing will go wrong.”
“How can you be sure?”
“I can be sure because I have studied the probabilities. And I can be sure because I know exactly what we are dealing with.”
“And what’s that?”
“An outmoded police force,” the deaf man said.
“They weren’t so outmoded when they sent me to jail,” Rafe said quietly, glumly.
“Examine the Police Department, if you will,” the deaf man said. “There are approximately thirty thousand cops in this sprawling metropolis. And this figure includes all of them, inspectors, deputy inspectors, detectives, patrolmen, veterinarians, policewomen, everything. The total police force numbers thirty thousand. That’s it.”
“So?”
“So there are approximately ten million people in this city. And it is the task of those thirty thousand policemen to see that those ten million people do not commit various criminal acts against each other. If we divide the number of potential lawbreakers by the number of policemen, we can say—roughly—that each cop is responsible for the conduct of about three hundred thirty-three people, am I right?”
Rafe did some laborious long division. “Yes, that’s about right.”
“Now, obviously, one cop—even assuming he is armed with the most modern weapons—couldn’t possibly control three hundred thirty-three people should they, for example, decide to commit three hundred thirty-three crimes in three hundred thirty-three places at the same time. It would be physically impossible for one cop to prevent all of those crimes because he couldn’t possibly be in two places at the same time, one of the basic laws of physics. But, of course, there are a vast number of policemen who, in combination, can be brought into action against a multitude of simultaneous criminal explosions. But even these men, in combination, could not cope with, if you will, ten million people committing ten million crimes simultaneously. Despite the permutations.”
“I don’t understand you,” Rafe said.
“Permutations,” the deaf man said. “The number of possible ways—well, let’s take a deck of cards. You’ll be more at ease with cards than with policemen. There are fifty-two cards in the deck. If we want to know how many possible ways there are of arranging those fifty-two cards, we start with the simple permutation, written this way.” He took a slip of paper from his pocket and quickly jotted: 52p52.
“I still don’t understand,” Rafe said.
“That’s simply the mathematical way of writing the permutations of 52. We callall the arrangements we can make by selecting all the numbers of a group ‘simple permutations.’ The equation becomes…” And he wrote: 52p52=52!
“That tells us how many possible ways there are of arranging a deck of 52 cards.”
“What’s the exclamation point for?” Rafe asked.
“It’s not an exclamation point. There are no interjections in mathematics. It simply indicates that the number must be multiplied by every whole number below it until we get to 1. For example, the number four followed by that symbol simply means 4 times 3 times 2 times 1.”
“So how many wayscan you arrange a deck of cards?”
“52! ways—or 52 times 51 times 50 times 49 times—well, all the way down until you reach the figure 1. It would take all day to multiply it out. But at the risk of making you nervous again, let’s get back to something of more concern to us, policemen. And, specifically, the detectives of the Eighty-seventh Squad. There are normally sixteen men on the squad. But when we pull our job, two will be on vacation and two will be in Washington taking an FBI course.”
“That leaves twelve,” Rafe said.
“Right. Let’s try to figure how many possible combinations those twelve men can arrange themselves into, shall we? The equation would be this.” He wrote: 12p12=12!
“Which means,” he went on, “12 times 11 times 10, and so on. Let’s see what that comes to.” Quickly, he began multiplying figures on his sheet of paper. “Well, here you are,” he said. “All the possible combinations for twelve men, 12 times 11 times 10 down through 1, is 479,001,600. It sounds staggering, doesn’t it?”
“It sure does. Evenone cop sounds staggering to me,” Rafe said.
“Of course, detectives usually work in pairs, and not in teams of twelve or eight or six or what have you. And this would automatically limit the number of possible combinations. Besides, we need not concern ourselves with the permutations of those twelve men. We need only to abstract a theory about law enforcement and crime prevention. It seems to me, Rafe, that the police operate on their own limited theory of probability. Obviously, with their inadequate force of thirty thousand, they cannot possibly hope to be everywhere at once. This is a damned big city and a great many people in it are practicing criminals. So the police operate against percentages. They figure in this fashion, more or less: A certain number of criminals must escape detectionfor the moment because we can’t possibly hope to be where they are when a crime is being committed or because we can’t successfully investigate every crime even after it’s been committed; however,in the long run, we will one day catch a previously undetected criminal because we will be in the right place at the right time or because the situation for a successful investigation will present itself.‘In the long run’ —those are the key words in probability.”