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Bunuel
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M22-16 02 Sep 2024, 17:19
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tanuja91
­So I read this as a combination question, vs a permutation one since the question asks for how many integers such that each digit is unique, i.e. 798 = 789 so we would have to exclude these overlaps...it would have helped if the question prompt included an example of what would meet the criteria to make sure the question is clear.
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­While 798 and 789 both consist of unique digits, the numbers themselves are different and should therefore be counted as two separate numbers.
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TheVDR
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M22-16 19 Sep 2024, 08:43
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tanuja91
­So I read this as a combination question, vs a permutation one since the question asks for how many integers such that each digit is unique, i.e. 798 = 789 so we would have to exclude these overlaps...it would have helped if the question prompt included an example of what would meet the criteria to make sure the question is clear.
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798 and 789, both are two separate, distinct numbers which fits the criteria "each digit is unique".
This doesn't mean that 798 = 789 = 897 = 879 and so on. If the number is in XYZ format then, X is not equal to Y is not equal to Z is the criteria....whereas XYZ, YXZ, ZXY are each separate entities.
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M22-16 20 Sep 2024, 15:10
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999-710=289

711
717

722
727

We see a trend 2 each tens, then:
for 700s + 800s + 900s:
9*2+10*2+10*2-3

-3 because 777, 888, 999 is just a number each

Then we have the 770, 771, 772... 880, 881,...
So, since we already got 777,888,999,
We have
9+9+9

So:
289-(9*2+10*2+10*2-3+9+9+9)=207
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M22-16 28 Sep 2024, 07:12
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Bunuel
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Why is 3*9*8 used to determine the amount of numbers that are from 700-799 and with three different integers?

(3 options for the first digit): 7, 8, or 9.

(9 options for the second digit): all digits except the one digit we used above.

(8 options for the third digit): all digits except the two digits we used above.

Check Constructing Numbers, Codes and Passwords Questions in our Special Questions Directory.

Hope it helps.
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Hi, when the question has said 3 different integers, why are we allowing 7 as the first digit?
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Bunuel
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M22-16 28 Sep 2024, 07:44
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idkquant
Bunuel
mrosale2
Bunuel or All,

Why is 3*9*8 used to determine the amount of numbers that are from 700-799 and with three different integers?

(3 options for the first digit): 7, 8, or 9.

(9 options for the second digit): all digits except the one digit we used above.

(8 options for the third digit): all digits except the two digits we used above.

Check Constructing Numbers, Codes and Passwords Questions in our Special Questions Directory.

Hope it helps.

Hi, when the question has said 3 different integers, why are we allowing 7 as the first digit?
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Why shouldn’t 7 be allowed as the first digit? The question asks for numbers greater than 710, so 7 can be the first digit. We are simply looking for numbers greater than 710 with different digits. For example, 718, 795, and 861 are all acceptable.
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M22-16 21 Jan 2025, 21:52
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I like the solution - it’s helpful.
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