How many postive intergers less than 4000 with no repeated digits can be formed where each digit is either 2,3,4,5 or 6?
The answer is 133 however i do not understand the working out at all..
The answer of 133 can be found by using the following formula:
5^3 x 4 = 400
400 is the total number of possible combinations of three digits, each digit being either 2, 3, 4, 5, or 6. However, since the digits cannot be repeated, we must subtract the number of combinations that contain repeated digits.
To calculate the number of combinations with repeated digits, we can use the following formula:
3^3 x 2 = 36
36 is the total number of possible combinations of three digits, two of which are the same.
Therefore, the total number of combinations with no repeated digits is 400 - 36 = 364.
Since there are 4000 positive integers less than 4000, the total number of positive integers with no repeated digits is 4000 - 364 = 3,636.