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  • How many different four-digit numbers can be formed using the prime numbers less then 15 if repetition is allowed and one's position is filled with the perfect square of 2?  

How many different four-digit numbers can be formed using the prime numbers less then 15 if repetition is allowed and one's position is filled with the perfect square of 2?

 

Option: 1

362


Option: 2

546


Option: 3

216


Option: 4

310


Answers (1)

To calculate the number of different four-digit numbers that can be formed using the prime numbers less than 15, with repetition allowed and the one's position filled with the perfect square of 2, we can proceed as follows:

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

For the thousands position, we can choose any prime number less than 15. The prime numbers less than 15 are 2, 3, 5, 7, 11, and 13. Since repetition is allowed, we have six options.

For the hundreds position, we can again choose any prime number less than 15. With repetition allowed, we have six options.

For the ten's position, we can choose any prime number less than 15. With repetition allowed, we have six options.

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 one's position = 1 (since it is fixed as 4)

Number of choices for the thousands position = 6 (any of the six prime numbers less than 15)

Number of choices for the hundreds position = 6 (any of the six prime numbers less than 15)

Number of choices for the ten's position = 6 (any of the six prime numbers less than 15)

Total number of different four-digit numbers = Number of choices for the one's 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 6 \times 6 \times  6

= 216

Therefore, there are 216 different four-digit numbers that can be formed using the prime numbers less than 15, with repetition allowed and the one's position filled with the perfect square of 2 (4).

 

Posted by

Ramraj Saini

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