The number of ways such that three penguins and six puffins stand in line so that all the puffins stand together is 17,280.
We are given two animals. The number of penguins is 3. The number of puffins is 6. We need to find out the number of ways that three penguins and six puffins can stand in line so that all the puffins can stand together.
We will use the concepts of permutations and combinations. We will make a bundle of all the puffins as a single entity.
The number of ways to arrange 6 puffins among themselves is 6! = 720. The number of ways to arrange 3 penguins and a bundle of puffins is (3 + 1)! = 4! = 24.
The total number of ways to form the line is the product of the above-mentioned calculation.
N = 720*24
N = 17,280
Hence, the number of ways such that three penguins and six puffins stand in line so that all the puffins stand together is 17,280.
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