Mathematics
Log
loga (1) = 0 because a exp 0 = 1 loga (a) = 1 because a exp 1 = a loga a exp x = x
Factorial Problem 1
How many different ways can the letters in the word “document””” be arranged?
For this problem we simply take the number of letters in the word and find the factorial of that number. This works because each letter in the word is unique and we are simply finding the maximum amount of ways 8 items can be ordered.
8!=8765432*1= 40,320
Factorial Problem 2
How many different ways can the letters in the word “physics” be arranged?
This problem is slightly different because there are two “s” letters. To account for this we divide by the number of duplicate letters factorial. There are 7 letters in the word physics and two duplicate letters so we must find 7!/2!. If the word had multiple duplicates, as in “little,” the formula would be 6!/(2! * 2!).
7!/2!=(7654321)/(2*1)= 2,520