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- How many different three-digit numbers can be formed using the prime numbers less than 25 if repetition is not allowed and one'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 25 if repetition is not allowed and one's position is filled with the square root of n, where n=9?
22
56
44
10
Answers (1)
To calculate the number of different three-digit numbers that can be formed using the prime numbers less than 25, 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 hundreds position, we can choose any prime number less than 25 except 3, as repetition is not allowed. The prime numbers less than 25 (excluding 3) are 2, 5, 7, 11, 13, 17, 19, and 23. Therefore, we have eight options for the hundreds position.
For the ten's position, we can again choose any prime number less than 25 except 3 and the prime number chosen for the hundreds position. Since repetition is not allowed, we have seven options for the ten'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 one's position = 1 (since it is fixed as 3)
Number of choices for the hundreds position = 8 (any of the eight prime numbers less than 25 except 3)
Number of choices for the ten's position = 7 (any of the seven prime numbers less than 25 except 3 and the prime number chosen for the hundreds position)
Total number of different three-digit numbers = Number of choices for the one's position Number of choices for the hundreds position
Number of choices for the ten's position
= 1 8
7
= 56
Therefore, there are 56 different three-digit numbers that can be formed using the prime numbers less than 25, with repetition not allowed and the one's position filled with the square root of 9 (3).
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