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The total number of 9-digit numbers which have all different digits is
- a)10 (9!)
- b)8 (9!)
- c)9 x (9!)
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The total number of 9-digit numbers which have all different digits is...
The number is to be of 9 digits
The first place can be filled in 9 ways only (as 0 can not be in the left most position )
Having filled up the first place the remaining 8 places can be filled in 9×8×7×...×1=9! ways
Hence total number of 9 digit numbers with distinct digits is =9×9!
The first place can be filled in 9 ways only (as 0 can not be in the left most position )
Having filled up the first place the remaining 8 places can be filled in 9×8×7×...×1=9! ways
Hence total number of 9 digit numbers with distinct digits is =9×9!
Most Upvoted Answer
The total number of 9-digit numbers which have all different digits is...
The total number of 9-digit numbers with different digits can be calculated using the concept of permutations.
Permutations: Permutation is an arrangement of objects in a specific order. In this case, we need to find the number of permutations of the digits 1-9 to form a 9-digit number.
Explanation:
1. The first digit of the 9-digit number can be any of the 9 digits (1-9), as there are no restrictions on the first digit.
2. After selecting the first digit, the second digit can be any of the remaining 8 digits, as we need to use different digits.
3. Similarly, the third digit can be any of the remaining 7 digits, the fourth digit can be any of the remaining 6 digits, and so on.
4. Therefore, the total number of permutations of the 9 digits is given by:
9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
which is equal to 9!
5. Hence, the correct answer is option C, 9!
Permutations: Permutation is an arrangement of objects in a specific order. In this case, we need to find the number of permutations of the digits 1-9 to form a 9-digit number.
Explanation:
1. The first digit of the 9-digit number can be any of the 9 digits (1-9), as there are no restrictions on the first digit.
2. After selecting the first digit, the second digit can be any of the remaining 8 digits, as we need to use different digits.
3. Similarly, the third digit can be any of the remaining 7 digits, the fourth digit can be any of the remaining 6 digits, and so on.
4. Therefore, the total number of permutations of the 9 digits is given by:
9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
which is equal to 9!
5. Hence, the correct answer is option C, 9!
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The total number of 9-digit numbers which have all different digits isa)10 (9!)b)8 (9!)c)9 x (9!)d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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