Question

Кошка имеет 7 котят : белое , черное, рыжее , черно белое, рыже черное, рыже белый, рыже черно белое. сколькими способами можно выбрать 4 котенка так, чтобы любые два из них имели общий цвет в своей прелести

Answer 1

1 способ:черный,черно белое, рыже черное,рыже черно белое.
2 способ:  белое черно белое,  рыже белый, рыже черно белое.
3 способ:  рыжее , рыже черное, рыже белый, рыже черно белое.

Answer 2

1)можешь просто взять 4 котенка и один цвет точно будет одинаковым

Answer 3

Problem Analysis

The problem states that a cat has 7 kittens with different colors: white, black, ginger, black and white, ginger and black, ginger and white, and ginger black and white. The task is to determine the number of ways to choose 4 kittens such that any two of them have a common color.

Solution

To solve this problem, we can consider the different color combinations and count the number of ways to choose 4 kittens with common colors.

1. White: There is only one white kitten. We need to choose 4 kittens, so we cannot choose all white kittens. Therefore, we can ignore this case.

2. Black: There is only one black kitten. We need to choose 4 kittens, so we cannot choose all black kittens. Therefore, we can ignore this case.

3. Ginger: There is only one ginger kitten. We need to choose 4 kittens, so we cannot choose all ginger kittens. Therefore, we can ignore this case.

4. Black and White: There is one black and white kitten. We need to choose 4 kittens, so we cannot choose all black and white kittens. Therefore, we can ignore this case.

5. Ginger and Black: There is one ginger and black kitten. We need to choose 4 kittens, so we cannot choose all ginger and black kittens. Therefore, we can ignore this case.

6. Ginger and White: There is one ginger and white kitten. We need to choose 4 kittens, so we cannot choose all ginger and white kittens. Therefore, we can ignore this case.

7. Ginger, Black, and White: There is one ginger, black, and white kitten. We need to choose 4 kittens, so we cannot choose all ginger, black, and white kittens. Therefore, we can ignore this case.

Therefore, we need to consider the cases where we have at least two kittens of the same color.

1. Two Kittens of the Same Color: We can choose any two kittens of the same color in 7C2 ways (7 choose 2). This can be calculated as follows:

   7C2 = 7! / (2! * (7-2)!) = 7! / (2! * 5!) = (7 * 6) / (2 * 1) = 21
   

2. Three Kittens of the Same Color: We can choose any three kittens of the same color in 7C3 ways (7 choose 3). This can be calculated as follows:

   7C3 = 7! / (3! * (7-3)!) = 7! / (3! * 4!) = (7 * 6 * 5) / (3 * 2 * 1) = 35
   

3. Four Kittens of the Same Color: We can choose all four kittens of the same color in 7C4 ways (7 choose 4). This can be calculated as follows:

   7C4 = 7! / (4! * (7-4)!) = 7! / (4! * 3!) = (7 * 6 * 5 * 4) / (4 * 3 * 2 * 1) = 35
   

Finally, we can add up the number of ways to choose 4 kittens with at least two kittens of the same color:

Total number of ways = 21 + 35 + 35 = 91

Therefore, there are 91 ways to choose 4 kittens such that any two of them have a common color.

Answer

There are 91 ways to choose 4 kittens from the given 7 kittens such that any two of them have a common color.