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  • How many numbers with 4 digits have exactly one 7 in the number?Option: 1 1792 <strong

How many numbers with 4 digits have exactly one 7 in the number?

Option: 1

1792 


Option: 2

4504 


Option: 3

2673

 


Option: 4

3274


Answers (1)

best_answer

The digit 0 cannot be placed at the first digit to make it a 4-digit number. 

There are 4 possible cases: 

Case 1: 

There is only one option for the digit 7, and there are nine options each for the second, third, and fourth digits (0–9, with the exception of 7).

Thus,

1\times 9\times 9\times 9=729

Case 2: 

With 8 options for the first position (one through nine except seven), 1 option for the second digit, 9 options for the third digit (0-9 except seven), and 9 options for the fourth digit (0-9 except seven), the digit seven is placed in second place.

Thus,

8\times 1\times 9\times 9=648

So, the number is 648. 

Case 3: 

With 8 options for the first position (1–9 except 7), 9 options for the second position (0–9 except 7), 1 option for the third position, and 9 options for the fourth position (0–9 except 7), the digit 7 is placed in third place.

Thus,

8\times 9\times 1\times 9=648

So, the number is 648. 

Case 4: 

With 8 options for the first position (1–9 except 7), 9 options for the second position (0–9 except 7), 9 options for the third position (0–9 except 7), and 1 option for the fourth position, the digit 7 is placed in fourth place.

Thus,

8\times 9\times 9\times 1=648

So, the number is 648. 

Hence, the total number is given by,

729+648+648+648=2673

Therefore, the total number is 2673.

 

Posted by

Ritika Harsh

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