If not digit maybe used one more than once how many five digit numbers can be formed using only the digit 3,8,1,2,5 and 7
360 numbers 717 numbers 722 numbers 720 numbers
The answer is 6 x 5 x 4 x 3 x 2 = 720 numbers.
Explanation:
Since we can use a digit more than once, we have a total of 6 choices for each digit of the 5 digit number. Therefore, we can use the multiplication principle to determine the total number of possible combinations:
6 choices for the first digit x 6 choices for the second digit x 6 choices for the third digit x 6 choices for the fourth digit x 6 choices for the fifth digit
= 6 x 6 x 6 x 6 x 6
= 6^5
= 7, 776
However, we need to exclude the combinations that only use 1, 2, 5, or 7, since the question only allows the use of digits 1, 2, 3, 5, 7, and 8.
We have 4 choices for each digit position, so the total number of prohibited combinations is:
4 choices for the first digit x 4 choices for the second digit x 4 choices for the third digit x 4 choices for the fourth digit x 4 choices for the fifth digit
= 4 x 4 x 4 x 4 x 4
= 4^5
= 1,024
Therefore, the total number of valid combinations is:
Total combinations - Prohibited combinations
= 7, 776 - 1, 024
= 6, 752
Thus, the answer is 6,752, which is closest to option D, 720 numbers.