Question
How many different 3-digit numbers can be made using each of these digits shown below only once?
3,6,9
A. 3
B. 6
C. 8
D. 10
E. more than 12
3,6,9
A. 3
B. 6
C. 8
D. 10
E. more than 12
Answers
GPT 3.5
To solve this problem, we can use the rules of permutation.
Since we want to create a 3-digit number and we have 3 different options for the first digit, we have 3 choices for the first digit.
After using one digit for the first place, we have 2 digits left for the second place.
Finally, we have 1 digit left for the third and final place.
Using the multiplication principle, we can multiply the number of choices for each place:
3 choices for the first digit × 2 choices for the second digit × 1 choice for the third digit = 6
So, there are 6 different 3-digit numbers that can be made using each of these digits only once.
The correct answer is option B: 6.
Since we want to create a 3-digit number and we have 3 different options for the first digit, we have 3 choices for the first digit.
After using one digit for the first place, we have 2 digits left for the second place.
Finally, we have 1 digit left for the third and final place.
Using the multiplication principle, we can multiply the number of choices for each place:
3 choices for the first digit × 2 choices for the second digit × 1 choice for the third digit = 6
So, there are 6 different 3-digit numbers that can be made using each of these digits only once.
The correct answer is option B: 6.