Question
How many different 3-digit numbers can be made using ,begin emphasis,each,end emphasis, of these digits shown below ,begin emphasis,only once?,end emphasis,
Information
,begin bold,3, 6, 9,end bold,
Answer options with 5 options
A.
3
B.
6
C.
8
D.
10
E.
more than 12
Information
,begin bold,3, 6, 9,end bold,
Answer options with 5 options
A.
3
B.
6
C.
8
D.
10
E.
more than 12
Answers
GPT-4o mini
To find the number of different 3-digit numbers that can be made using each of the digits 3, 6, and 9 exactly once, we can analyze the problem as follows:
1. **Determine the digits available:** We have three distinct digits: 3, 6, and 9.
2. **Forming 3-digit numbers:** A 3-digit number can be formed by arranging all three digits in different orders.
3. **Calculating permutations:** The number of ways to arrange 3 distinct digits is calculated using the factorial of the number of digits, which is 3! (3 factorial).
Calculating 3!:
\[
3! = 3 \times 2 \times 1 = 6
\]
Thus, there are **6 different 3-digit numbers** that can be formed using the digits 3, 6, and 9, each used only once.
So, the answer is:
**B. 6**
1. **Determine the digits available:** We have three distinct digits: 3, 6, and 9.
2. **Forming 3-digit numbers:** A 3-digit number can be formed by arranging all three digits in different orders.
3. **Calculating permutations:** The number of ways to arrange 3 distinct digits is calculated using the factorial of the number of digits, which is 3! (3 factorial).
Calculating 3!:
\[
3! = 3 \times 2 \times 1 = 6
\]
Thus, there are **6 different 3-digit numbers** that can be formed using the digits 3, 6, and 9, each used only once.
So, the answer is:
**B. 6**