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  • How many different six-digit numbers can be formed using the whole numbers less than 9 if repetition is not allowed and one's position is filled with the square root of n, where n=9?

How many different six-digit numbers can be formed using the whole numbers less than 9 if repetition is not allowed and one's position is filled with the square root of n, where n=9?

 

Option: 1

2120


Option: 2

2166


Option: 3

2144


Option: 4

2401


Answers (1)

best_answer

To calculate the number of different six-digit numbers that can be formed using the whole numbers less than 9, with repetition not allowed and the one's position filled with the square root of 9, we can proceed as follows:

The square root of 9 is 3, so for the one's position, we have only one option, which is 3.

For the ten-thousands, thousands, hundreds, ten's, and thousands position, we can choose any whole number less than 9 except 3, as repetition is not allowed. The whole numbers less than 9 (excluding 3) are 1, 2, 4, 5, 6, 7, and 8. Therefore, we have seven options for each of these positions.

Therefore, the number of different six-digit numbers that can be formed is obtained by multiplying the choices for each position:

Number of choices for the one's position = 1 (since it is fixed as 3)

Number of choices for the ten-thousands, thousands, hundreds, ten's, and thousands position = 7 (any of the seven whole numbers less than 9 except 3)

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

= 1\times 7 \times7\times 7\times 7\times 7

= 2401

Therefore, there are 2401 different six-digit numbers that can be formed using the whole numbers less than 9, with repetition not allowed and the one's position filled with the square root of 9 (3).

 

Posted by

manish painkra

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