Question

В корзине лежит 8 морковок, 6 картошке, 5 огурцов. Сколькими способами можно выбрать 4 овоща из корзины? Сколькими способами можно выбрать 1 морковку и 2 картошки? Срочно, даю 20 баллов!!

Answer 1

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Answer 2

Number of Ways to Choose 4 Vegetables from the Basket

To determine the number of ways to choose 4 vegetables from the basket, we can use the concept of combinations. In this case, we have 8 carrots, 6 potatoes, and 5 cucumbers in the basket.

The formula for calculating combinations is:

C(n, k) = n! / (k! * (n - k)!)

Where: - n is the total number of items in the set (in this case, the total number of vegetables in the basket). - k is the number of items to be chosen (in this case, 4).

Using this formula, we can calculate the number of ways to choose 4 vegetables from the basket:

C(8+6+5, 4) = (8+6+5)! / (4! * (8+6+5 - 4)!)

Simplifying the equation:

C(19, 4) = 19! / (4! * 15!)

Now, let's calculate the result:

C(19, 4) = (19 * 18 * 17 * 16) / (4 * 3 * 2 * 1) = 38,760

Therefore, there are 38,760 different ways to choose 4 vegetables from the basket.

Number of Ways to Choose 1 Carrot and 2 Potatoes

To determine the number of ways to choose 1 carrot and 2 potatoes from the basket, we can again use the concept of combinations. In this case, we have 8 carrots and 6 potatoes in the basket.

The formula for calculating combinations is the same as mentioned earlier:

C(n, k) = n! / (k! * (n - k)!)

Where: - n is the total number of items in the set (in this case, the total number of vegetables in the basket). - k is the number of items to be chosen