Question 42557: How many four-digit numerical codes can be created if no digit may be repeated?
Thanks
Answer by psbhowmick(878)   (Show Source):
You can put this solution on YOUR website! As it is a numerical code consisting of 4 digits so the first digit can be 0.
But if it were a 4-digit number then the first digit could not be 0 as then the number becomes a 3 digited number.
The first digit can be selected from any one of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 numerals.
So it can be chosen in 10 ways.
After the first digit is chosen we can select the second digit from 9 digits.
This is because that the very digit which was chosen as the first digit cannot chosen as the second digit as no digit can be repeated.
For each of the 10 ways of selecting the first digit, the second digit can be selected in 9 ways.
So the first two digits can be selected in 10 x 9 = 90 ways.
The third digit can be selected in 8 ways and based on the same logic as above.
For each of the 90 ways of selecting the first two digits, the third digit can be selected in 8 ways.
So the first three digits can be selected in 90 x 8 = 720 ways.
Following exactly the same procedure, the first four digits i.e. all the codes possible can be selected in 720 x 7 = 5040 ways.
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