Question

How many six digit even numbers are possible if the leftmost digit cannot be zero

Answer 1

The six digit numbers are the numbers from 100,000 to 999,999.

There are 900,000 of these numbers.

Half of those are even, so there are 450,000 six digit even numbers.

Answer 2

450000 six digit even numbers are possible if the leftmost digit cannot be zero.

Explanation:

We have to find Total six digit even numbers.

To form an even of 6 digit we have 10 digits to place in first 5 position starting from left most, here repetition is allowed so, No ways of doing this is
`10^5` and number of ways selecting one digit from 5 digit for ones place is [/tex]^{5}\textrm{P}_{1}=\farc{5!}{(5-1)!}=\frac{5!}{4!}=5[/tex]

So, Total even numbers =
`10^5*5=500000`

This includes number which has zero on the left most place.

To get these numbers we fir 0 at place 2 left 4 places has 9 options and ones place has 5 options as before.

So, Number of such cases =
`10^4*5=50000`

Thus, total Number of 6 Digit number even number = 500000 - 50000 = 450000

Therefore, 450000 six digit even numbers are possible if the leftmost digit cannot be zero.