00:01
Alright, so for this question, we are given the set of numbers 0, 1, 2, 3, and 4, and we need to make a positive odd 4 -digit number without repeating the digits, right? so the way we approach this is, so one of the requirements we're given is that the number has to be odd.
00:24
In order for a number to be odd, right, one of these two digits has to be at the end in our given.
00:30
Set only one and three are odd numbers so if we draw out blanks for representing our four -digit number that we're making from these digits given then this last digit here can only be a one or three giving it two possibilities so from there right so from there what you can do is you realize one of these odd numbers is now going to be used you don't know which one but one of them is so now we can go to the front right because in the front you can't have a zero as a first number otherwise this will no longer be a four -digit number it'll be a three -digit number with zero in the front so uh the possibilities for here are two four and then one of the odd numbers so you know you have two odd numbers here one of them is gone so that means you have one odd number left so you have three different possibilities now for this first blank.
01:38
All right, then moving on to now our second and third blank.
01:43
So the key in these two blanks is now you can have zero back into play.
01:47
So as euro can once again be a valid number.
01:52
So from there we're going to do is just notice that the second blank has a set of zero.
02:00
And then so we had three numbers here, right? three possibilities two four or an odd number and now you realize if one of these gets selected it doesn't matter which one if one of them gets selected you now have two more options so it's going to be zero and then some number and then another number right so we don't know they could be both even it could be a two and a four two and odd or four and odd um so it could be any combination of those three numbers but since we've already used one of them, we only have two available now.
02:37
But since we also have the added zero, we once again have three possibilities for this second blank.
02:45
And then finally, for this third blank, we're using the same principle that we did to figure out this situation right here, in that we know from zero, x, and y, one of those three has already been selected.
02:58
It could be the y, it could be x, it could be the zero.
03:02
So from there we realize now we only have two options here.
03:06
So we have x and y.
03:10
And so i realize this could be a little bit confusing.
03:13
So instead of saying x and y, i'll say here we have a set of two numbers.
03:23
And here we have a set of three numbers.
03:31
Right...