Question

To gain access to his account, a customer using an automatic teller machine (ATM) must enter a 6-digit code ( 0 to 9). If repetition of the same digit is not allowed (for example, 555561 or 333333), how many possible combinations are there?(The first digit can not be zero)

a)151200 b)136080 c)1,000,000 d)900,000

Answer 1

Given that repetition is not allowed and the first number can not be zero.

          1              2                   3                    4              5              6

Suppose this is the representation of 6 digit code.

Now we can not use zero at first place we can fill it with the other 9 numbers. So 9 ways.

For 2nd place, we cannot use the number which we use in the first place but can use zero at the 2nd place. So 9 ways.

Similarly 3rd place. 8 ways

4th place, 7 ways.

5th place, 6 ways.

6th place, 5 ways.

The total number of combination which is possible is 9*9*8*7*6*5 = 136080 ways.