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  • How many different four-digit numbers can be formed using the digits 1, 4, 5, 6, 7, 8, and 9 if repetition is allowed and hundred's position is filled with the number 1?  <di

How many different four-digit numbers can be formed using the digits 1, 4, 5, 6, 7, 8, and 9 if repetition is allowed and hundred's position is filled with the number 1?

 

Option: 1

443


Option: 2

343


Option: 3

223


Option: 4

563


Answers (1)

best_answer

To calculate the number of different four-digit numbers that can be formed using the digits 1, 4, 5, 6, 7, 8, and 9, with repetition allowed and the hundred's position filled with the number 1, we can proceed as follows:

For the hundred's position, since it is fixed as 1, we have only one option.

For the thousands position, any of the seven available digits can be chosen (1, 4, 5, 6, 7, 8, or 9) since repetition is allowed.

For the ten's position, any of the seven available digits can be chosen as well.

For the one's position, any of the seven available digits can be chosen.

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 hundred's position = 1 (since it is fixed as 1)

Number of choices for the thousands position = 7 (since any of the seven digits can be chosen)

Number of choices for the ten's position = 7 (any of the seven digits can be chosen)

Number of choices for the one's position = 7 (any of the seven digits can be chosen)

Total number of different four-digit numbers = Number of choices for the hundred's position \times Number of choices for the thousands position \times Number of choices for the ten's position \times Number of choices for the one's position

= 1\times 7 \times 7\times 7

= 343

Therefore, there are 343 different four-digit numbers that can be formed using the digits 1, 4, 5, 6, 7, 8, and 9, with repetition allowed and the hundred's position filled with the number 1.

 

Posted by

shivangi.bhatnagar

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