If no digit can be used more than once, how many 5-digit numbers can be formed only using the numbers 3,8,1,2,5, and 7?
A: 350 numbers
B: 717 numbers
C: 722 numbers
D: 720 numbers
I guessed the answer 720 and got it right but I don't know why the answer is 720. Can someone please explain to me how to complete this problem?
You can use combination.
There are 6 digits: 3, 8, 1, 2, 5, 7
So the combination digits will be:
6*5*4*3*2 = 720
To find the number of 5-digit numbers that can be formed using the given digits, we need to consider the following:
1. The first digit can be any of the six given digits (3, 8, 1, 2, 5, 7). Hence, we have six choices for the first digit.
2. Since no digit can be repeated, once the first digit is chosen, we have five digits left to choose from for the second digit.
3. Similarly, once the first two digits are chosen, we have four digits left to choose from for the third digit.
4. Following the same logic, once the first three digits are chosen, we have three digits left to choose from for the fourth digit.
5. Lastly, once the first four digits are chosen, we have two digits left to choose from for the fifth digit.
Therefore, the total number of possibilities is given by multiplying the number of choices for each digit:
6 choices for the first digit × 5 choices for the second digit × 4 choices for the third digit × 3 choices for the fourth digit × 2 choices for the fifth digit = 6 × 5 × 4 × 3 × 2 = 720.
So the correct answer is D: 720 numbers.