Question

For many locks used in gyms, the owner can set a six digit pass code to lock it. A. How many digits could you choose from for the first number of the pass code if it cannot begin with 0 or 1? How many digits could you choose from for the second number of the pass code? Assume that the numbers cannot be repeated. How many different six digit pass codes are possible if the numbers in the pass code cannot be repeated?

Answer 1

We want to make a 6 digits pass code.

We have 0-9 i.e. 10 numbers to choose from, for every digit.

1) However, for the first digit we cannot choose 0 or 1. Therefore, we are left with the remaining 8 choices from 2-9.

2) Now, if the numbers cannot be repeated, I cannot choose the number I selected for the first digit again. But, I can now choose 0 or 1. This means, I can not choose the digit I chose before, but, all the remaining 9 digits are available. So, we have 9 choices for the second digit.

3) Summarising, we have 8 choices for first digit.

9 choices for second digit.

Now, for the third digit I'm left with 8 choices(excluding the digits I chose for the first two digits)

Similarly, for the fourth digit, I will have 7 choices and so on.

Total number of ways = 8×9×8×7×6×5 = 120960