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The total number of 9 digit numbers which have all different digits is ______.

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Question

The total number of 9 digit numbers which have all different digits is ______.

Options

  • 10!

  • 9!

  • 9 × 9!

  • 10 × 10!

MCQ
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Solution

The total number of 9 digit numbers which have all different digits is 9 × 9!.

Explanation:

We have to form 9 digit numbers from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

And we know that 0 cannot be put on extremely left place.

So, first place from the left can be filled in 9 ways.

Now repetition is not allowed.

So, the remaining 8 places can be filled in 9!

∴ So, the remaining 8 places can be filled in 9 × 9!

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Chapter 7: Permutations and Combinations - Exercise [Page 125]

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NCERT Exemplar Mathematics Exemplar [English] Class 11
Chapter 7 Permutations and Combinations
Exercise | Q 38 | Page 125

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