What is P(8, 5) and how is it different from 8^5.
P(8, 5) is the number of permutations of 5 elements drawn from a set containing 8 elements. Here, repetition is not allowed, each of the letters chosen is unique and it is only used once in a permutation.
8^5 is the number of ways of arranging 5 elements from a set of 8 elements where there is no restriction on the number of times each element can be used. As there are 8 different elements to choose from, each of the 5 elements chosen can take on 8 different values.
P(8, 5) = 6720 while 8^5 = 32768