"Enzo," she said, "what’s the probability that the three chosen customers all pick the same topping?"
"So most of the time," Marco laughed, "the pizza is a mix of three distinct flavors!" That night, a boy named Luca asked the most curious question: "What if you drew the names without replacement from a total of 20 customers, but then the three chosen still pick toppings with repetition? And also, before picking toppings, you shuffle a deck of 40 Scoppia cards (Italian regional cards: four suits, numbered 1 to 10). If the first card is a '1' of any suit, you cancel the pizza game. If not, you proceed. What’s the chance we actually make a pizza?"
Just then, the bell rang. Three new customers entered: a nun, a clown, and a beekeeper. Calcolo combinatorio e probabilita -Italian Edi...
"Now that’s combinations without repetition for the selection, but with permutations for the picking order," Enzo explained.
Every Saturday, Enzo offered a — a mystery pizza with random toppings chosen by a strange ritual. Customers would write their names on slips of paper, and Enzo would draw three names. Those three would each choose a topping from a list of ten: funghi, carciofi, salsiccia, peperoni, olive, cipolle, acciughe, rucola, gorgonzola, zucchine . "Enzo," she said, "what’s the probability that the
Enzo nodded. "It happened once. A trio of truffle enthusiasts. The pizza was… intense." A burly farmer named Marco asked, "What about the chance that all three toppings are different?"
In the narrow, lantern-lit streets of Perugia, old Enzo ran the most beloved pizzeria in Umbria. But Enzo had a secret: he was also a mathematician who had retired early from the University of Bologna. If not, you proceed
Number of ways to choose 3 distinct customers in order: [ 20 \times 19 \times 18 = 6840 ] (This step doesn’t affect the probability of making a pizza because it’s always possible to pick toppings regardless of who they are. The only cancelling event is the card draw.)