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  • How many different three-digit numbers can be formed using the prime numbers less than 20 if repetition is not allowed and hundred's position is filled with the square root of n, where n=9?

How many different three-digit numbers can be formed using the prime numbers less than 20 if repetition is not allowed and hundred's position is filled with the square root of n, where n=9?

 

Option: 1

42


Option: 2

56


Option: 3

24


Option: 4

30


Answers (1)

best_answer

To calculate the number of different three-digit numbers that can be formed using the prime numbers less than 20, with repetition not allowed and the hundred's position filled with the square root of 9, we can proceed as follows:

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

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

For the one's position, we can again choose any prime number less than 20 except 3 and the prime number chosen for the ten's position. Since repetition is not allowed, we have six options for the one's position.

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 hundred's position = 1 (since it is fixed as 3)

Number of choices for the ten's position = 7 (any of the seven prime numbers less than 20 except 3)

Number of choices for the one's position = 6 (any of the six prime numbers less than 20 except 3 and the prime number chosen for the ten's position)

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

= 1 \times 7 \times 6

= 42

Therefore, there are 42 different three-digit numbers that can be formed using the prime numbers less than 20, with repetition not allowed and the hundred's position filled with the square root of 9 (3).

 

Posted by

Ajit Kumar Dubey

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