Please solve

[fc135]

All of the stocks are designated by either a 4 digit code or a 5 digit letter code that is created by using 26 letters of the alphabet. Which of the foll gives the maximum no: of different stocks?

(1) 2(26^5)
(2) 26(26^4)
(3) 27(26^4)
(4) 26(26^5)
(5) 27(26^5)

[Rahul@gurome]

Number of ways in which a four digit code can be created using 26 letters of the alphabet is (26^4).
Number of ways in which a 5 digit code can be created using 26 letters of the alphabet is (26^5).
So maximum number of different codes we can have is (26^4) + (26^5) = (26^4)(1+26) = (26^4)*27 = 27(26^4).
The correct answer is (3).

[amising6]

stocks designated by 4 digit code
will be
26*26*26*26(i.e 26 alphabet can take 1st place 26 alphabet can take 2nd place till 4 place code)
i.e 26^4
similiarly
stocks designated by 5 digit code
will be
26*26*26*26*26(i.e 26 alphabet can take 1st place 26 alphabet can take 2nd place till 5 place code)
i.e 26^5
so maximum number of stock will be 26^4+26^5
i.e 26^4(1+26)
i.e 27*26^5