ques no 15
ques no 15We will have an even number when the units digit is either 2 or 4
Case 1: Unit digit is 2
suppose 1000th digit is 1
we have total 6 numbers such that it is ending with 2 and starting with 1
similarly for 3,5,4
so
1000x(1+3+4+5)x6
also if 1 is on 100th and 10th place we have 6 each
and total numbers with 2 at its unit place is 24
so total sum
1000x(1+3+4+5)x6+100x(1+3+4+5)x6+10x(1+3+4+5)x6+1x(2)x24
=86628
Case 1: Unit digit is 4
suppose 1000th digit is 1
we have total 6 numbers such that it is ending with 4 and starting with 1
similarly for 3,5,2
so
1000x(1+3+2+5)x6
also if 1 is on 100th and 10th place we have 6 each
and total numbers with 4 at its unit place is 24
so total sum
1000x(1+3+2+5)x6+100x(1+3+2+5)x6+10x(1+3+2+5)x6+1x(4)x24
=73356
total=159984
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