Multiple choice

The number of different codes formed by three letters of English alphabet followed by a three digit number is $\displaystyle (26)^{3}\times900 $ (if repetitions are allowed)

  1. Both (A) & (R) are individually true & (R) is correct explanation of (A),

  2. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).

  3. (A)is true but (R) is false,

  4. (A)is false but (R) is true.
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A Correct answer
AI explanation

To construct the code, each of the three letter positions can be filled in 26 ways because repetitions are allowed, yielding 26^3 arrangements. The three digit number must range from 100 to 999, giving 900 possible numbers. By the multiplication principle, the total number of codes is the product of these independent choices, which is 26^3 x 900. This validates the given statement.

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