A company assigns product codes consisting of all the letters in the alphabet.How many product codes...
A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 7 letters in its codes, and all letters can be repeated in any one code?
Answer/Solution
E.8353082582
Steps/Work
The no of ways in which the company can make codes of 1 letter : 26
# for 2 letters : 26*26 = 676
# for 3 letters : 26 * 26*26 =17576
# for 4 letters : 26 * 26*26*26 =456976
# for 5 letters : 26 * 26*26*26*26 =11881376
# for 6 letters : 26 * 26*26*26*26*26 =308915776
# for 7 letters : 26 * 26*26*26*26*26*26 =8031810176
The total : By adding all of them , 26+676+17576+456976+11881376+308915776+8031810176
=8353082582
E
# for 2 letters : 26*26 = 676
# for 3 letters : 26 * 26*26 =17576
# for 4 letters : 26 * 26*26*26 =456976
# for 5 letters : 26 * 26*26*26*26 =11881376
# for 6 letters : 26 * 26*26*26*26*26 =308915776
# for 7 letters : 26 * 26*26*26*26*26*26 =8031810176
The total : By adding all of them , 26+676+17576+456976+11881376+308915776+8031810176
=8353082582
E