00:01
In this question we want to find the number of four digit numbers where the leading number is not zero and they are all distinct digits and with one digit being nine.
00:14
So there are two cases.
00:16
Case one, the first digit is nine.
00:19
In case two, the first digit is not nine, not zero either.
00:28
Now, in general, if i have n distinct objects and i want to arrange in a row it will be n factorial ways let's look at the three digits in here it will have the digits from 0 to 8 so there are 9 digits so from the 9 digits i will choose 3 to place into these 3 slots n now n is times or is plus n so there's a thumps there is 3 factorial ways to arrange these 3 digits in a row among these three slots.
01:22
And so 9 choose 3 times 3 factorial, it's 84 times 6 and that will be 504.
01:30
So that's case 1.
01:32
Case 2.
01:35
Among these three slots, one of them has to be the number 9.
01:42
So suppose i just put the number 9 here.
01:48
Okay, now let's back to the first slot.
01:51
The first slot, the number is not 9 and not 0.
01:54
So it's from 1...