The number of permutations of n objects taken r at a time is given by the formula:
P(n, r) = n! / (n - r)!
Where "!" denotes the factorial function.
In this case, we have 3 bases and we want to find the number of permutations possible when all 3 bases are used. We can use the formula above with n = 3 and r = 3:
P(3, 3) = 3! / (3 - 3)! = 3! / 0! = 6 / 1 = 6
This gives us the number of permutations when only 3 bases are used. However, we want to find the number of permutations when all 3 bases are used. Each permutation of 3 bases can be ordered in 3! = 6 different ways. Therefore, the total number of permutations possible when all 3 bases are used is:
6 x 6 = 36
Hence, the number of permutations possible when three bases are used is 36, which is equal to 64 when raised to the power of 1.5 (sqrt(36) = 6, and 6^3 = 64).