Question

How many different three-digit numbers can be written using digits from the set 1, 2, 3, 4, 5 without any repeating digits?

1. MichaelMet
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.