Find the number of strings of length eight of distinct lette

Find the number of strings of length eight of distinct letters of the alphabet so that the words do not have both A and B in them.

Solution

Count of the number of words of length eight that contain both A and B.
8 * 7* P(24,6) -eq 1

Total number of words of length eight are P(26,8) -eq 2

Therefore, number of strings of length eight of distinct letters of the alphabet so that the words do not have both A and B in them are :

eq 2 - eq 1

=> P(26,8) - 8 * 7* P(24,6)