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Suppose a potter has 15 choices of glazes to apply on her pottery. She knows that if she applies glaze A OVER glaze B, it may not look the same as applying glaze B OVER glaze A. She wants to test the effect of combining these glazes by dipping a small vessel into 3 of these glazes. She will dip deeply into the first glaze (to see how it looks alone), then less deep into the next glaze (to see how it looks when applied OVER the first glaze) and then barely dip into the third glaze (to see how it looks when applied OVER the previous two glazes).

Required:
How many possible test vessels can be glazed?

Respuesta :

LammettHash

The potter probably doesn't want to apply the same glaze multiple times, in which case she has 15 choices for the first layer, 14 for the second, and 13 for the third, giving

15 * 14 * 13 = 2730

possible test vessels.

On the other hand, it's possible that the potter is fine with re-using the first glaze in the third layer. In that case, whichever glaze is used first is not counted among the options for the second layer, but it comes back for the third layer, so that there would be

15 * 14 * 14 = 2940

test vessels.