Permutations and Combinations 09
That evening, while the whole family was gathered together, Awang shared the results of his morning’s efforts. However, Ashiu had long lost interest in her husband’s “findings,” and at times, impatiently retorted, “Can your ‘findings’ put food on the table?” before rising to attend to the household chores.
But tonight was different. Awang even took out the leftover strong liquor from a few days ago, which he and Old Ma hadn’t finished. He insisted on sharing the drink with his wife to celebrate some good news. The thin fabric of Ashiu’s coat trembled as if mocking him rhythmically, yet when she caught the sudden seriousness in her husband’s eyes, the shaking ceased.
“I understand permutations and combinations,” Awang began, “but according to Qian Xiaohao’s calculations, it’s hopeless.
“Take this Seven-Star Lottery, for example. Seven positions, each with ten possibilities. Using the method we learned in high school, that’s ten to the power of seven, meaning the chance of winning with a single ticket is one in a million. Each ticket costs two yuan, so to guarantee a win, you’d have to buy every possible combination in the same draw, spending two million yuan. Winning the jackpot of five million yuan would still leave you with much less after taxes. This is the most basic calculation, and practically, it’s too cumbersome. One mistake could invalidate all tickets for that draw. Besides, the lottery updates so rapidly that if you don’t buy all one million tickets within two days, the effort is wasted.”
Hearing this, the smile vanished from Ashiu’s face, replaced by a solemn gaze fixed on Awang.
“So buying a million tickets for the same draw is impossible, unrealistic. But there’s another point you have to consider,” Awang continued after taking a sip of water.
“Since the first Seven-Star Lottery draw until now, there have been tens of thousands of draws, and no number combinations have ever repeated, right? Also, these seven numbers have an order—have there been any reverse sequences? Or repeats with more than three numbers? Add to that some special numbers, and what about the occurrence of four or more consecutive numbers? Not to mention four, even three consecutive numbers have never appeared so far!”
“Could you explain that more clearly? I’m having trouble following,” Ashiu said anxiously.
“In short, out of the one million possible combinations, nearly half can be eliminated through calculation—meaning they won’t win. If we buy those numbers with a high probability of winning, we have a strong chance of hitting the five million jackpot. I’ve done a rough calculation in my head—if I carefully filter and select using pen and paper, we can spend the least amount of money to win the jackpot. Do you understand, my dear? And it’s not just for one draw. The important thing is, as time goes on and more numbers get eliminated, the money we need to spend decreases, and the chances of winning increase!”
Awang waved the bottle of white liquor excitedly, like a great scientist unveiling his discovery to the world. His wife, Ashiu, looked at him with tears in her eyes, as though witnessing a divine revelation reborn.
Meanwhile, outside the house, Aren was also animatedly gesturing, but he did not confront Awang directly. Quietly, he slipped back home, knowing that the time to strike a deal had finally arrived.