Question

How many seven-digit numbers are even and have a 3 in the hundreds place?

Please explain this and how to understand the basic concept about this? step by step would be good too and with examples if you can. appreciate this. thank you.

Answer 1

A seven digit even number

means it must start without 0 and end with 0,2,4,6,8

Therefore,

There are 9 choice ( 1 to 9) for first digit,

5 choice for last digit

Also we have condition that 3 in the hundreds place

therefore only one option for hundreds place

and rest other digit have 10 choice( 0 to 9)

Thus

Total numbers of ways,

9*10*10*10*1*10*5 =450000

OR

Let consider ABCDEFG is 7 digit number,

A must be in between 1 to 9, so there are 9 choice,

G must be even so there are 5 choice

E must be 3 so there are only 1 choice

B C D F be any digit between 0 to 9 so 10 choice

Thus

Total number of ways are

9*10*10*10*1*10*5 = 450000