How many 3-digit numbers can be formed by using the digits 1 to 9… - Vidyadip

Question

How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?

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Answer

There are 9 ways to pick the 1st digit. For each of those 9 ways there are 8 ways to choose the second digit. That's 9 × 8 or 72 ways to pick the first two digits. For each of those 72 ways there are 7 ways to choose the third digit. That's 72 × 7 ways or 504 ways to pick all three digits.

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