A certain identification code is a list of five symbols: S1,S2,D1,D2,D3. Each of the first 2 symbols must be one of the

Question

A certain identification code is a list of five symbols: S1, S2, D1, D2, D3. Each of the first 2 symbols must be one of the 26 letters of the English alphabet, and each of the last 3 symbols must be one of the 10 digits. (Repeated letters and digits are allowed.) What is the total number of different identification codes?  
    
(A) 1,757,600  
(B) 676,000  
(C) 468,000  
(D) 1,676  
    
#greprep #GRE

Vijaya Lakshmi K · Answer

Hello Ishita,

There are 5 places to fill S1, S2, D1, D2 and D3 respectively. Repetition is allowed

S1: can take value from 26 alphabets (26 options)
S2: can take value from 26 alphabets (26 options)
D1: can take value from 10 digits (10 options)
D2: can take value from 10 digits (10 options)
D3: can take value from 10 digits (10 options)

Total no of possibilities = S1×S2×D1×D2×D3S1×S2×D1×D2×D3= 26×26×10×10×1026×26×10×10×10 = 676,000.

Hence B is the correct option.

Hope this helps. All the Best!

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