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| 1. |
How many 4-digit numbers are there with no digit repeated |
| Answer» Let 4 digit number be abcdThe choices do we have for the digit aWe have 9 choices (since the first digit cannot be 0).Now for each possible choice of a we have 9 choices for b (since we want b to be a different digit to a and we now allow 0 ).So for choice of the ab part we have 9∗9=81 possibilities.Now for each of these we have 8 choices for c (to avoid c being the same as either a or b). For each of these we have 7 choices for d (to avoid d being the same as either a,b or c ).So in total there are 9∗9∗8∗7=4536 possible numbers. | |