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  • How many different three-digit numbers can be formed using the prime numbers less then 10 if repetition is allowed and ten's position is filled with the perfect square of 3?<div class='qna-

How many different three-digit numbers can be formed using the prime numbers less then 10 if repetition is allowed and ten's position is filled with the perfect square of 3?

Option: 1

12


Option: 2

16


Option: 3

14


Option: 4

30


Answers (1)

To calculate the number of different three-digit numbers that can be formed using the prime numbers less than 10, with repetition allowed and the ten's position filled with the perfect square of 3, we can proceed as follows:

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

For the hundreds position, we can choose any prime number less than 10. The prime numbers less than 10 are 2, 3, 5, and 7. Since repetition is allowed, we have four options.

For the one's position, we can again choose any prime number less than 10. With repetition allowed, we have four options.

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

Number of choices for the ten's position = 1 (since it is fixed as 9)

Number of choices for the hundreds position = 4 (any of the four prime numbers less than 10)

Number of choices for the one's position = 4 (any of the four prime numbers less than 10)

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

= 1 \times 4\times 4

= 16

Therefore, there are 16 different three-digit numbers that can be formed using the prime numbers less than 10, with repetition allowed and the ten's position filled with the perfect square of 3 (9).

 

Posted by

Kshitij

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