Finding how many possible combinations

Question

There are 8 standard classifications of blood type. An examination for prospective laboratory technicians consists of having each candidate determine the type for 3 blood samples. How many different examinations can be given if no 2 of the samples provided for the candidate have the same type?

Answer 1

There are 8 possible classifications, and three samples are to be tested for classification.

 

In the Real World, the succession of results for tests 1 through 3 might be AAA, or ABA, etc... Visualize it as 8 possibile classifications for sample 1, and again for sample 2, and also for sample 3.  So it's 8 cubed = 2⁹ =512 possible results.

 

However, in the UNUSUAL statement that you're working with, no classifications can repeat so you have 8(7)(6) also known as ₈P_{3 =}

_336.