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A three-digit number is formed using digits from 1-5
How many even numbers can be formed using three different digits?
Always choose the most restrictive digit first.
That would be the last digit, which can only be 2 or 4.
We can choose the last digit 2 ways.
We then choose the first digit as any of the 4 remaining digits.
We then choose the middle digit as any of the 3 remaining digits.
Answer (2)(4)(3) = 24 ways.
How many even numbers can be formed if digits may be repeated?
We can choose the last digit 2 ways, as 2 or 4.
We then choose the first digit as any of the 5 digits.
We then choose the middle digit as any of the 5 digits.
Answer (2)(5)(5) = 50 ways.
How many multiples of five can be formed if digits can be repeated?
We can choose the last digit 1 way, as 5.
We then choose the first digit as any of the 5 digits.
We then choose the middle digit as any of the 5 digits.
Answer (1)(5)(5) = 24 ways.
Edwin
