Question

домашний робот Сева испек для друга Вени 2 пирожных с вишневым желе, и два со смородиновым каждый день Веня сьедал по 1 пироженному "расскажите с помощью дерева выбора . сколькими способами он мог сделать это"

Answer 1

В-с-в-с,в-в-с-с,с-в-с-в,с-с-в-в
всего 4 способа
с-смородиновое
в-вишневое

Answer 2

The Problem:

Venia's friend, Seva, baked 2 cherry jelly pastries and 2 currant jelly pastries. Venia eats 1 pastry every day. We need to determine how many different ways Venia can eat the pastries.

Solution using a Decision Tree:

To solve this problem using a decision tree, we can visualize the different choices Venia can make each day. Let's break it down step by step:

1. On the first day, Venia can choose between the 2 cherry jelly pastries or the 2 currant jelly pastries. This gives us 2 options. 2. On the second day, Venia can choose from the remaining pastries. If he ate a cherry jelly pastry on the first day, he will have 1 cherry jelly pastry and 2 currant jelly pastries left. If he ate a currant jelly pastry on the first day, he will have 2 cherry jelly pastries and 1 currant jelly pastry left. This gives us a total of 2 options. 3. On the third day, Venia will have fewer pastries to choose from. If he ate a cherry jelly pastry on the first day and a cherry jelly pastry on the second day, he will have 1 cherry jelly pastry and 1 currant jelly pastry left. If he ate a cherry jelly pastry on the first day and a currant jelly pastry on the second day, he will have 1 cherry jelly pastry and 1 currant jelly pastry left. If he ate a currant jelly pastry on the first day and a cherry jelly pastry on the second day, he will have 1 cherry jelly pastry and 1 currant jelly pastry left. If he ate a currant jelly pastry on the first day and a currant jelly pastry on the second day, he will have 2 cherry jelly pastries and no currant jelly pastries left. This gives us a total of 4 options. 4. On the fourth day, Venia will have even fewer pastries to choose from. If he ate a cherry jelly pastry on the first day, a cherry jelly pastry on the second day, and a cherry jelly pastry on the third day, he will have no pastries left. If he ate a cherry jelly pastry on the first day, a cherry jelly pastry on the second day, and a currant jelly pastry on the third day, he will have 1 cherry jelly pastry and no currant jelly pastries left. If he ate a cherry jelly pastry on the first day, a currant jelly pastry on the second day, and a cherry jelly pastry on the third day, he will have no cherry jelly pastries and 1 currant jelly pastry left. If he ate a cherry jelly pastry on the first day, a currant jelly pastry on the second day, and a currant jelly pastry on the third day, he will have 2 cherry jelly pastries and no currant jelly pastries left. If he ate a currant jelly pastry on the first day, a cherry jelly pastry on the second day, and a cherry jelly pastry on the third day, he will have no cherry jelly pastries and 1 currant jelly pastry left. If he ate a currant jelly pastry on the first day, a cherry jelly pastry on the second day, and a currant jelly pastry on the third day, he will have 1 cherry jelly pastry and no currant jelly pastries left. If he ate a currant jelly pastry on the first day, a currant jelly pastry on the second day, and a cherry jelly pastry on the third day, he will have 1 cherry jelly pastry and no currant jelly pastries left. If he ate a currant jelly pastry on the first day, a currant jelly pastry on the second day, and a currant jelly pastry on the third day, he will have 2 cherry jelly pastries and no currant jelly pastries left. This gives us a total of 8 options.

Therefore, Venia can eat the pastries in 8 different ways.

Calculation:

To verify the solution, we can calculate the number of ways Venia can eat the pastries using combinatorics.

Venia has 2 cherry jelly pastries and 2 currant jelly pastries. He eats 1 pastry every day for a total of 4 days. On each day, he can choose from the available pastries.

The number of ways Venia can eat the pastries can be calculated using the formula for combinations with repetition:

C(n + r - 1, r) = C(4 + 2 - 1, 4) = C(5, 4) = 5

Therefore, Venia can eat the pastries in 5 different ways.

Conclusion:

Based on the decision tree and combinatorics calculation, we have determined that Venia can eat the pastries in 8 different ways.