N Choose K

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#22 - N Choose K

Every Autumn, when the leaves begin to fall, my family goes on walks around our neighborhood to collect leaves. With the leaves, we do arts and crafts. When we do this, we always look for a variety of shapes, each coming from a different species. There are such a variety of native trees in the Pacific Northwest and since learning to identify them, I have wondered what different varieties of leaf combinations would be possible to create. After returning from a walk, I realized I could utilize one of my favorite formulas to create placemats!

n = total number of items, r = number of selected items

Within a 20 foot radius of the telephone pole outside my house, I found the following leaves.

Using the number of leaves, we calculate the number of combinations of leaves I could gather if I selected three leaves at random.

With the natural variety of leaves outside my house, there are 20 different combinations if I select three leaves at random! My favorite four combinations are below. There is one for each member of my household’s placemat.

That variety of leaves in my neighborhood amazes and delights me. My exploration is limited by the fact I may have identified the leaves wrong as a result of their coloring, decay, abnormalities, or my inexperience. For example, if I identified two of the same species of a leaf as different leaves, this could lead my calculations to be off.

References

City of Seattle Department of Planning and Development. (2015, August). Seattle DPD - Common Seattle Trees. Seattle.