If repetition of the digit is allowed then the number of even natural number having three digit is
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The numbers are 100, 102, 104, ....., 998
This is an ap with a=100 and d=2
nth term=998
We need to find n
a+(n-1)d = 998
100+(n-1)2=998
By solving we get n=450
.......................
Another way
The ones place can have only 0,2,4,6 and 8. So there are 5 options. For tens place any digit fro 0 to 9 can come. So 10 options. For hundreds place any digit except 0 can come. So 9 options.
So total =9*10*5 = 450
This is an ap with a=100 and d=2
nth term=998
We need to find n
a+(n-1)d = 998
100+(n-1)2=998
By solving we get n=450
.......................
Another way
The ones place can have only 0,2,4,6 and 8. So there are 5 options. For tens place any digit fro 0 to 9 can come. So 10 options. For hundreds place any digit except 0 can come. So 9 options.
So total =9*10*5 = 450
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