Question

You need to create a four-digit password using 0-9.

How many passwords are possible, without repeating a number, if a password must not start with a 0?

Answer 1

Solution:

We have to create a four-digit password using 0-9.

First Digit

Second Digit

Third Digit

Fourth Digit

We have to find how many passwords are possible, without repeating a number, if a password must not start with a 0.

If a password must not start with a 0, that means first digit should be one of 1 to 9 digits

thus for first digit we have 9 ways.

We do not repeat this first selected digit for next places. Thus we have 8 digits from 1 to 9 for next place.

Now for second place , third place and fourth place we can select 0.

Thus total digits for second place are 0 and 8 = 9 ( we are not adding 0 and 8, we are counting 0 and 8 digits = 9 digits)

Now for third place we have 9- 1 = 8

and for fourth we have 8 - 1 = 7

Thus

First Digit	Second Digit	Third Digit	Fourth Digit
9	9	8	7

Thus

Total number of possible passwords are = 9 X 9 X 8 X 7

Total number of possible passwords are = 4536