Alice has 3 apples, 4 bananas, and 2 cherries. If she eats one piece of fruit per day for a week, in how many different orders can she eat the fruit?

Sun, 03 May 2026 21:11:45 +0000

**How Many Ways Can Alice Eat Her Weeknight Fruit? Solving a Simple, Popular Puzzle** Ever wondered how many unique ways someone could savor a handful of fruit—just one piece a day—over a week? Think of Alice, with three crisp apples, four juicy bananas, and two juicy cherries. Her daily choice becomes a surprising combinatorial puzzle with real-world relevance. This isn’t just a riddle—people are exploring these sorta-intuitive questions because they blend daily habits with mathematical curiosity, especially as more users engage with interactive learning on platforms like Google Discover. At first glance, Alice’s fruit set — three apples, four bananas, two cherries — seems straightforward: eat one fruit daily for seven days. But calculating the exact number of different eating orders reveals a neat combination problem. The formula for permutations of multiset objects applies here. With 9 total pieces of fruit (3 + 4 + 2), but eating only 7, the real focus is sequencing choices across the week—choosing which fruit appears each day while avoiding repetition beyond available counts. This puzzle offers a tangible, accessible way to explore permutations without complexity. To break it down:
- Alice has 9 total fruit pieces
- She eats exactly 7, selecting from 3 apples, 4 bananas, 2 cherries
- Each order matters, but repetitions are limited by availability