A code consists of 3 distinct letters followed by 2 distinct digits. How many such codes can be formed from the 26 English letters and the 10 digits (0-9)?
Answer and explanation
Correct answer: A. 1404000
- Step 1: Number of ways to choose and arrange 3 distinct letters: P(26, 3) = 26 25 24 = 15600.
- Step 2: Number of ways to choose and arrange 2 distinct digits: P(10, 2) = 10 * 9 = 90.
- Step 3: Total codes = 15600 * 90 = 1404000.
Answer
1404000.
Why not the others: 1560000 computes 15600 100 (allowing digit repetition); 1757600 allows both letter and digit repetition (26^3 10^2); 1260000 computes using 25 24 23 * 90.
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