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How many 2-digit numbers can be formed from the set of digits of the number $72372$?

My try :

The set of digits of $72372={{2,3,7}}$

The number of 2-digit numbers =$3×3=9$ "with repetition"

And $3×2=6$ "without repetition"

Is that right ?

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  • $\begingroup$ The answers assume you only have one "3" available, while your calculations assume that there are two. So you are right, the answers below are right, but the answers are differrent. The problem text is unclear on this and it is thereofre a bad problem. $\endgroup$ – Arthur Dec 1 '17 at 9:04
  • $\begingroup$ @Arthur i need to know if "set of digits of the number " makes any difference here ? $\endgroup$ – user373141 Dec 1 '17 at 9:06
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    $\begingroup$ I can't read minds. You have to ask whoever wrote the original problem, there is no one else who can give you a conclusive answer. $\endgroup$ – Arthur Dec 1 '17 at 9:08
  • $\begingroup$ Why are you so nervous? @Arthur $\endgroup$ – user373141 Dec 1 '17 at 9:11
  • $\begingroup$ I'm not. I'm telling you that you have made an assumption that may be correct, it may not. Under that assumption, your answer is correct, yes. But whether that assumption is correct is not something anyone can tell you, except the person who made the problem. $\endgroup$ – Arthur Dec 1 '17 at 9:18
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There are two $2$, two $7$, and one $3$:

$$22, 23, 27 $$

$$32, 37$$

$$72,73,77$$

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  • $\begingroup$ But we have "set of digits of the number " which equals {2,3,7} , should it make any difference? $\endgroup$ – user373141 Dec 1 '17 at 9:04
  • $\begingroup$ I see, I think that depends on how we interpret the question. I interpret is as you have two $2$, two $7$, and one $3$, put them inside a bag. What are the numbers that you can form if you draw two numbers without replacement. If you interpret the question as from $\{2,3,7\}$ , then your answer is correct. $\endgroup$ – Siong Thye Goh Dec 1 '17 at 9:07
  • $\begingroup$ You can use combination formula too $\endgroup$ – Atharva Shetty Dec 1 '17 at 9:32
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Digits on form XX = // {77, 22}// = 2.

Digits on form XY = {2,3,7}{2,3,7} = 3*2 = 6

So 2 + 6 = 8.

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