Using the principle of counting ,
Total 648 , three-digit positive numbers are there such that all three digits are different and the first digit is not zero.
Counting principle: If an event occurs m times and another event occurs n times, the total number of occurrences of the event is m × n.
Let the three-digit number be abc.
Since, 3-digit numbers cannot have a 0, in the hundreds place i.e., c place. The first left most digit (a) can be any number from 1 to 9. Hundreds place can be entered in 9 ways. The 10ᵗʰ digit (i.e., b ) can contain a zero, but can not use the digit on 100ᵗʰ place(i.e., a ).So, there is also 9 ways to enter 10ᵗʰ digit. Similarly, the ones place( i.e., c) can contain zero digits, but the 100ᵗʰ and 10ᵗʰ placed digits cannot. So, there are 8 ways to fill the ones place.
Then, according to counting principles, the total possible three digit number is 9×9×8 = 648
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