00:01
In this problem, it is said that you are creating a four -digit pin code.
00:05
We need to determine how many choices there are.
00:08
Now in the first case, it is said that we have no restrictions.
00:13
So we want a four -digit pin code, so there are a total of four digits.
00:18
And there are no restrictions.
00:19
So that means we have 10 options to choose from for the first digit, because we have a total of 10 digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
00:28
And there are no restrictions, so there are 10 options for the second digit, 10 options for the third digit, and 10 options for the 4 digit as well.
00:36
Using the multiplication rule of counting, if we multiply these numbers, we will have the number of ways of selecting these 4 digits, and so we will have the total number of choices.
00:47
So we end up with 10 ,000.
00:50
So there are a total of 10 ,000 choices in this case.
00:54
In the next problem, once again we have four digits.
01:00
However, this time it is said that no digit is repeated.
01:04
So that means for the first digit, we have 10 options to choose from.
01:08
We can choose any digit we want from 0 to 9.
01:11
And for the second digit, we can choose any digit except for the one which we chose over here, because no digit can be repeated.
01:19
So that's 10 minus 1 a total of 9 options to choose from.
01:22
For the third digit, we can choose any digit except for the two digits over here.
01:29
So we have 10 minus 2, a total of 8 options.
01:32
Similarly, for the 4 digit, we can choose any digit except for the 3 digits we chose in these 3 places.
01:40
So that's 10 minus 3 a total of 7 options...