Question

How many 9 digit numbers have their first and last digits even?

Answer 1

Answer: 200,000,000.

we have 9 spaces we need to fill in

There are 10 total numbers(0–9)

There are 5 even numbers(0,2,4,6,8)

fill from left to right

u cannot start with 0 so pick another number 2,4,6,8 any of those

4*10^7*5= 20*10^7 = 2*10^8

200,000,000.

Answer 2

There are 900000000 nine-digits numbers and exactly half of them have an even sum of digits (because every number can be paired with another of the opposite parity by changing the last digit).