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- How many different four-digit numbers can be formed using the digits 1, 3, 4, 5, 6, 7, 8, and 9 if repetition is allowed and ten's position is filled with the number 9?12 <d
How many different four-digit numbers can be formed using the digits 1, 3, 4, 5, 6, 7, 8, and 9 if repetition is allowed and ten's position is filled with the number 9?12
416
320
640
512
Answers (1)
To calculate the number of different four-digit numbers that can be formed using the digits 1, 3, 4, 5, 6, 7, 8, and 9, with repetition allowed and the ten's position filled with the number 9, we can proceed as follows:
For the ten's position, since it is fixed as 9, we have only one option.
For the thousands position, any of the eight available digits can be chosen (1, 3, 4, 5, 6, 7, 8, or 9) since repetition is allowed.
For the hundreds and one's position, any of the eight available digits can be chosen as well.
Therefore, the number of different four-digit numbers that can be formed is obtained by multiplying the choices for each position:
Number of choices for the ten's position = 1 (since it is fixed as 9)
Number of choices for the thousands position = 8 (since any of the eight digits can be chosen)
Number of choices for the hundreds position = 8 (any of the eight digits can be chosen)
Number of choices for the one's position = 8 (any of the eight digits can be chosen)
Total number of different four-digit numbers = Number of choices for the ten's position Number of choices for the thousands position
Number of choices for the hundreds position Number of choices for the one's position
= 1 8
8
8
= 512
Therefore, there are 512 different four-digit numbers that can be formed using the digits 1, 3, 4, 5, 6, 7, 8, and 9, with repetition allowed and the ten's position filled with the number 9.
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