how possible 6 digit PIN code with exactly 5 different numbers?

Question

how possible 6 digit PIN code with exactly 5 different numbers?

Answer 1

A,B,C,D, and E are the unique digits

R is the repeating digits...

A B C D E R where R=A or R=B or R=C or R=D or R=E, so there are 5 possibilities here thus far...

There are also 10 choices for A, 9 choices for B, 8 choices for C, 7 choices for D, 6 choices for E

So for this set up, there are 10*9*8*7*6*5 possibilities...

The repeating digit can occur in one of the 6 positions, and there are 6! ways to arrange them...

6! * 10*9*8*7*6*5 = 108,864,000

Answer 2

You have six independent digits, and five ways to choose each of them. We have five ways to choose the first digit, and five ways to choose the second digit. This makes 5*5=25 ways to choose the first two digits. That is, there are five ways to add a digit to a 1, five ways to add a digit to a 2, five ways to add a digit to a 3, five ways to add a digit to a 4, and five ways to add a digit to a 5. In total, this is 25 options.

likewise, we have 5 ways to choose the third digit and 25 ways to choose the first two digits — that is, five different ways to add onto each of the 25 options for the first two digits. Thus we have 5*25=125 ways to choose the first three digits.

similarly we have 625 = 5^4 ways to get the first four digits, 5^5 = 3125 ways to get the first five digits, and 5^6 = 15,625 ways to get the first six digits.

in general, the number of ways to get n digits out of m symbols is m^n