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2024 Math Kangaroo

Problem 6

Problem 6 · 2024 Math Kangaroo Medium
Counting & Probability careful-counting

Ria has three cards with the numbers 1, 5 and 11. She wants to place the cards next to each other to form a 4-digit number. How many different 4-digit numbers can she form?

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Answer: B — 4
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Hint 1 of 2
List the orders of the three cards and write out the number each makes.
Still stuck? Show hint 2 →
Hint 2 of 2
Two different orders can spell the same number, so count distinct numbers, not orders.
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Approach: list the distinct numbers the three cards can spell
  1. Placing cards 1, 5, 11 in a row always gives a 4-digit number.
  2. Writing out the orders gives 1511, 1115, 5111, and 1151 (some orders repeat).
  3. The distinct numbers are 1511, 1115, 5111, 1151.
  4. That is 4 different numbers.
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