An identification number is a sequence of 6 digits (0 – 9). A digit may repeat. The number of identification numbers that start with 012 or 123 or 234 or 345 is
There are total 10 digits from 0 to 9. So number of ways to select one digit from 0 to 9 is 10. Let's first find the number of ways to arrange the digits such that the identification number starts with 012.
The first digit of identification number should be 0 and number of ways to select this digit is only 1. Similarly number of ways to select second and third digit is also 1 because it should compulsorily be 1 and 2, respectively.
Now, the fourth digit can be anything from 0 to 9, so number of ways to select the fourth digit is 10. Similarly for fifth and sixth digit, number of ways to select, is also 10 because any digit can be selected from 0 to 9.
Now, according to multiplication rule if an event can occur in x different ways and another event can occur in y different ways, after first event has been occurred, the total number of events will be .
So using multiplication rule, total number of ways to make identification numbers starting with 012 will be multiplication of number of ways in which each digit can place.
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