Question

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How many positive three-digit integers have at least one digit that is a 5 or a 7?

Answer 1

Answer:

• 452 integers

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Three-digit integer in the form of abc.

Possible numbers for each digit

• a - 1 to 9, nine options,
• b and c - 0 to 9, ten options

Let a = 5 or 7, then for a we have 2, for b and c 10 options:

• 5bc or 7bc

• 2*10*10 = 200

Let b = 5 or 7, then for a we have 9 - 2 = 7, for b 2 and for c 10 options

• a5c or a7c
• 7*2*10 = 140

Let c = 5 or 7, then for a we have 9 - 2 = 7, for b 10 - 2 = 8 and for c 2 options

• ab5 or ab7
• 7*8*2 = 112

Total options

• 200 + 140 + 112 = 452