Problem Solving

All of the stocks on the OTC market are designated by either a 4-letter or a 5-letter code that is created using 26 letters of the english alphabets. Which of the following gives the maximum number of stocks that can be designated with these codes?

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

Thanks.

OA: C

rkhicha wrote:All of the stocks on the OTC market are designated by either a 4-letter or a 5-letter code that is created using 26 letters of the english alphabets. Which of the following gives the maximum number of stocks that can be designated with these codes?

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

Thanks.

OA: C

stock designated by 4 letter
- - - -
first position can be filled in 26 ways (26 alphabet)
second position can be filled in 26 ways (26 alphabet)
third position can be filled in 26 ways (26 alphabet)

fourth position can be filled in 26 ways (26 alphabet)
so total number of ways four 4 letter code
26*26*26*26
similirly for 5 letter code
26*26*26*26*26
so total number of ways
26^4+26^5
26^4(1_26)
26^4*27