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Counting and Basic Probability · Question 16 of 65

Question 16

HardOriginal question

A college issues parking stickers made of 2 letters from A to Z followed by 3 digits. The two letters must be different, the digits may repeat, and the first digit cannot be 0. How many stickers can be issued?

Options for question 16

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. Letters: 26×25=65026 \times 25 = 650 ordered pairs of different letters.

  2. Digits: first digit 9 ways, then 10 and 10, so 900900.

  3. Stickers =650×900=5,85,000= 650 \times 900 = 5{,}85{,}000.

Worth noting

6,08,400 is 26×26×90026 \times 26 \times 900, letting the letters repeat. 6,50,000 lets the digits start with 0, and 6,76,000 makes both mistakes.

Concept
Multiplication rule across letters and digits with different restrictions
Typical time
120 s
Your time
—
The rule this testsThe counting principle
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