kullayappayenugula wrote:hi Neelgandham,
I have a doubt regarding the foramtion of "three-digit numbers greater than 600 and with all distinct digits"
it is given as 4*9*8 = 288. But this includes numbers like 661,662,663,.....771,772,... etc.
can you please tell me what is wrong in my understanding here.
Hi!
Because you're multiplying by a smaller number, you've actually removed those duplicates.
Here's another way you could write the product:
(number of digits that could go in the first spot) * (number of digits that could go in the second spot that you haven't used yet) * (number of digits that could go in the third spot that you haven't used yet)
In the first spot, we have 6, 7, 8 and 9, for a total of 4 possible digits.
In the second spot, you have all 10 digits available (don't forget about 0); however, since you used one of them up in the first spot, there are only 9 digits left.
In the third spot, you have all 10 digits available; however, since you used one of them up in the first spot and a different one up in the second spot, there are only 8 digits left.
Accordingly, the number of non-digit repeating integers you can create is:
4*9*8 = 288
