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  • How many different six-digit numbers can be formed using the prime numbers less than 20 if repetition is not allowed and one's position is filled with the square root of n, where n=4? <p

How many different six-digit numbers can be formed using the prime numbers less than 20 if repetition is not allowed and one's position is filled with the square root of n, where n=4?

 

Option: 1

4560


Option: 2

5010


Option: 3

2401


Option: 4

3660


Answers (1)

best_answer

To calculate the number of different six-digit numbers that can be formed using the prime numbers less than 20, with repetition not allowed and the one's position filled with the square root of 4, we can proceed as follows:

The square root of 4 is 2, so for the one's position, we have only one option, which is 2.

For the ten-thousands, thousands, hundreds, and ten's position, we can choose any prime number less than 20 except 2, as repetition is not allowed. The prime numbers less than 20 (excluding 2) are 3, 5, 7, 11, 13, 17, and 19. 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 2)

Number of choices for the ten-thousands, thousands, hundreds, and ten's position = 7 (any of the seven prime numbers less than 20 except 2)

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

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

= 2401

Therefore, there are 2401 different six-digit numbers that can be formed using the prime numbers less than 20, with repetition not allowed and the one's position filled with the square root of 4 (2).

 

Posted by

manish painkra

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