Question

How many 20-digit numbers are such that the sum of their digits is even?

Answer 1

oh dear...this may take a while

Answer 2

even plus even causes even
and odd plus odd causes even

Answer 3

we need even number of odd numbers in order for the number to be positive

Answer 4

so all odd numbers for all 20 digits would be evan aka 20!

Answer 5

you can make the sum even by fixing the last digit

Answer 6

true

Answer 7

So total 20 digit numbers with even parity would be : 9*10^18*5

Answer 8

9 ways to choose first digit
10 ways to choose 2nd through 19th dgitis
5 ways to choose last digit

Answer 9

wouldn't you just use that thing were you take 20 and multiply it by 19 then mult that by 18 and so in

Answer 10

there are 10 digits in base10 system
so there are 10 digits to choose from for each position

Answer 11

however we cannot choose "0" as first digit , so only 9 choices for first digit