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1. 60 different three-digit numbers can be written using digits from the set 1, 2, 3, 4, and 5 without any repeating digits.

   What are numbers?

   • A number is a mathematical object that can be used to count, measure, and label things.
   • The natural numbers 1, 2, 3, 4, and so on are the original examples.
   • Number words can be used to represent numbers in language.

   To find how many different three-digit numbers can be written using digits from the set 1, 2, 3, 4, and 5 without any repeating digits:

   1st Method:

   • The 1st digit can be written in 5 ways
   • The 2nd digit can be written in 4 ways (since 1 already gone and no repetition)
   • The 3rd digit can be written in 3 ways (since 2 already gone and no repetition)
   • Total number of ways = 5x4x3 = 60 ways

   2nd Method:

   • Permutation (since ORDER MATTERS) of 3 digits chosen among 5 (with no repetition)
   • ⁵P₃ = (5!)/(5-3)! = (5!)/(2!) = 60 ways

   Therefore, 60 different three-digit numbers can be written using digits from the set 1, 2, 3, 4, and 5 without any repeating digits.

   Know more about numbers here:

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