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# ques no 15

Asked by chandanbr6004 12th December 2017, 11:22 PM

We 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

Answered by Expert 16th December 2017, 12:26 PM
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