Exercise · ZW-MULTIPLICATION-PRINCIPLE-002 · ★☆☆ Basic
A code has 2 letters (out of 26) followed by 3 digits (0 to 9). How many codes are there if repetitions are allowed?
Choose one option.
Show answer
- D. \(676000\)
Explanation
There are five steps: \(26\cdot 26\cdot 10\cdot 10\cdot 10=676000\). Adding the possibilities per position is the typical mistake.
Review the concept: Multiplication principle
If a task is done in successive steps and step \(i\) admits \(n_i\) options regardless of how the earlier steps were done, the total number of ways \(N\) is the product of those numbers.
\[N=n_1\cdot n_2\cdots n_k\]
More practice problems: multiplication principle
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- ZW-MULTIPLICATION-PRINCIPLE-005 A plate has 3 different letters (out of 26) followed by any 2 digits. How many plates are there?
- ZW-MULTIPLICATION-PRINCIPLE-006 How many functions are there from a 4-element set to a 3-element set?
- ZW-MULTIPLICATION-PRINCIPLE-007 How many even three-digit integers (100 to 999) are there?
- ZW-MULTIPLICATION-PRINCIPLE-008 Select the condition required to multiply the number of options of each step.
- ZW-MULTIPLICATION-PRINCIPLE-009 Without repeating digits, how many odd 4-digit numbers (1000 to 9999) are there?
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