Calcolo Combinatorio E Probabilita -italian Edi... -

Total possible ordered selections (without replacement from 20): (20 \times 19 \times 18 = 6840).

First person: 10 choices. Second: 9 choices (different from first). Third: 8 choices (different from first two). [ 10 \times 9 \times 8 = 720 ]

10 possible choices (all mushrooms, all onions, etc.) [ \frac{10}{1000} = \frac{1}{100} ]

Just then, the bell rang. Three new customers entered: a nun, a clown, and a beekeeper. Calcolo combinatorio e probabilita -Italian Edi...

"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?"

This is always possible once we reach this stage. So the probability that a pizza gets made is just the probability of not drawing a '1' first:

Probability (given no card cancellation): [ \frac{3000}{6840} = \frac{300}{684} = \frac{50}{114} = \frac{25}{57} \approx 0.4386 ] Third: 8 choices (different from first two)

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.

Enzo laughed. "Life is random, cara mia . But understanding the combinations helps you not fear the uncertainty."

The beekeeper picked honey (not on the menu), the nun picked mushrooms, the clown picked pineapple (scandalous). All different. "So most of the time," Marco laughed, "the

Enzo’s eyes sparkled. "Now that is combinatorics with constraints ."

"I bet," Chiara whispered, "the chance they all pick different toppings is 72%."

[ P(\text{pizza}) = \frac{9}{10} ]