How many 9-digit numbers of different digits can be formed? - Vidyadip

Question

How many 9-digit numbers of different digits can be formed?

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Answer

In a nine-digit number 0 cannot appear in the first digit. So, the number of ways of filling up the first digit = 9.
Now, 9 digits are left including 0. So, second digit can be filled with any of the remaining 9 digits in 9 ways.
Similarly, remaining digits can be filled in 8, 7, 6, 5, 4, 3 and 2 ways.
Hence, the total number of required numbers
= 9 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2
= 9 × (9!)

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