Number starts with 1= 5!
Number start with 2=5! Why not 4! According to GPT’s explanation we have 1,3,4,5,6 digits so we are taking 5! If it’s the case then for number starts with 3,we also could take 5! Instead of 4! I’m not getting the explanation even after reading it 2/3times. There’s still confusion. I’m sorry if I’ve asked a silly question
OK, so for all these numbers, we are comparing it to 321,000. The internal logic is that any 6 digit number starting with 1 or 2 will always be less than 321,000. Think about the 100 thousands or 200 thousands… any number in those ranges will be less than 321K.
Now numbers starting with 3 is a different story. We will find that some numbers will be less than the 321,000 reference, while others will be larger. Example: 312,456 < 321,000, but 361,245 > 321,000.
So we can’t apply the same logic that we did with 1’s and 2’s to 3’s. That is why we cant do 5! for the numbers starting with 3: not all of those #s will be less than 321,000. What rule can we use then? Well, within the 300 thousands (300K-400K), any number starting with 3 followed by 1, will be less than 321,000. Thats how we get 3 1 _ _ _ _. So any of these numbers 312,456 or 316,254 or whatever else are always less than 321,000.
Since this rule has 4 digits to interchange we get 4!. In this case we dont have to worry about a number like 320,500, which is less than 321,000. This is because of the limitation that we have to use all 6 numbers from 1 to 6 as our digits. So any number starting with 32 _ _ _ _ will be at least as large as 321000: 324156, etc.
Let me know if this makes sense!
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I appreciate your response but uhm ! I am trying to get the explanation but I still feel uncleared! Maybe after going through 5/6times, I’ll understand it. Thanks for your help
Which aspect is most confusing to you?
No no, now I am getting it. We can’t take 5! Because we may get some numbers bigger or smaller than the given number while the 100k or 200k is always going to be smaller than the given number, right? So we are taking 5!.
If there are similar cases like 700k /900k will we also consider the same approach ??
is this a permutation question and where did you get this question from?
Yes, K M F