On a desk, there are 6 sheets of blue paper, 4 sheets of yellow paper, 5 sheets of green paper, and 2 sheets of pink paper. In how many ways can the paper be stacked?
Answer (3)
In 240 ways paper can be stacked.
Given that, on a desk, there are 6 sheets of blue paper, 4 sheets of yellow paper, 5 sheets of green paper, and 2 sheets of pink paper.
We need to find how many ways can the paper be stacked.
What are permutations and combinations?
Arranging people , digits, numbers, alphabets, letters, and colours are examples of permutations . Selection of menu, food, clothes, subjects, and the team are examples of combinations.
Now, 6×4×5×2= 240 ways
Therefore, in 240 ways paper can be stacked.
To learn more about permutations and combinations visit:
https://brainly.com/question/13387529 .
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There are 17 sheets of paper of various colors, and since each sheet is distinct, the total number of ways these can be stacked is 17!, which equals 355,687,428,096,000 different combinations.
To determine the number of ways the paper can be stacked, we consider each sheet of paper as distinct, and the problem becomes a permutation problem. We have a total number of sheets as 6 (blue) + 4 (yellow) + 5 (green) + 2 (pink) = 17 sheets. Since no sheet is identical to another, we use the formula for calculating permutations of different items, which is n!, where n is the total number of items.
Thus, the number of ways to stack these 17 sheets of paper is 17!, which is the product of all positive integers up to 17. This results in a large number, specifically 355,687,428,096,000 ways to stack the paper. This number is so immense because each sheet can be in any of the 17 positions and for each position, there are remaining sheets that can be arranged in many different ways.
The total number of ways to stack the papers is 85,800, calculated using the permutations of a multiset formula. We considered the total number of sheets and accounted for identical sheets of different colors in our calculation. Using the factorial approach, we arrived at this result by dividing the factorial of the total number of sheets by the factorial of the number of sheets of each color.
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