Question

A code word is to consist of 2 English alphabets followed by 2 distinct numbers between 1 and 9. For example, CA23 is a code word. How many such code words are there?

• A. 615800
• B. 46800
• C. 719500
• D. 410800
• E. None of these

Answer 1

The correct option is B 46800

(i) There are in all 26 English alphabets. We have to choose 2 distinct alphabets. First alphabet can be selected in 26 ways. Second alphabet can be selected in 25 ways. Again, out of 9 digits (1 to 9), first digit can be selected in 9 ways. Second digit can be selected in 8 ways Thus, the number of distinct codes $26\times 25\times 9\times 8=46800.$