Question

four numbers for my set 0 to 9 including 0 9 are used to create a personal identification number once a numbers use it cannot be reused how many possible outcomes begin with a 0

Answer 1

All 4 digit numbers beginning with 0, start with 0000 and end with 0999.
The first 100 numbers will always repeat, as they will have more than one 0
The first number will be 0123
From 0100 to 0100 there are no numbers possible
From 0101 to 0999, there are 7 numbers out of every 10 that could be an outcome, 700/1000 numbers are possible
There are 700 out of 1000 that could be outcomes
70%
0.7

Answer 2

Answer: 504

Explanation:

Given : The number of digits used to make the personal identification number =10

The total digits in the personal identification number =4

If repetition of digits is not allowed then the number of possible outcomes is given by permutations .

The number of possible outcomes begin with a 0 is given by [ first place is fixed for 0, so we take 1 for it then apply permutation on the rest of 9 digits taking 3 at a time]:-

`1* {9}P_3=(9!)/((9-3)!)\\\\=(9*8*7*6!)/(6!)=10*9*8*7=504`

Hence, the possible number of outcomes =504