+0  
 
+1
94
7
avatar+392 

How many numbers less than 1000 are there that use only the digits of 2088?

 Jul 20, 2020
 #1
avatar+27660 
+1

I will assume you do not allow a leading zero

   this will be a 3 digit number to be less than 1000

     you have 3 choices for the first number  (since we cannot use zero)

        then you have 3 choices for the second number

          and finally 2 choices for the third number

              3 x 3 x 2 = 18 numbers BUT two of the choices are identical ('8' s)

                      so the options are divided by 2     18 / 2 = 9 numbers

 

Ok....incorrect...hmmmm

  no leading zero    so you have only two choices for the first digit   2  or  8

      then you have three choices for the next digit 

         and two for the last digit           12 numbers     (maybe?)   Just kinda guessing now. cheeky

 Jul 20, 2020
edited by ElectricPavlov  Jul 21, 2020
 #2
avatar+392 
+1

Nice try! But that's incorrect

 

12 is wrong, too :(

 Jul 21, 2020
edited by HelpBot  Jul 21, 2020
 #3
avatar
0

2088
4 nCr 1 =3 - But leading zero does not count 0, 2, 8 =2 
4 nCr 2 = 7 - But leading zeros do not count 02, 08, 20, 28, 80, 82, 88 =5 
4 nCr 3 = 12 - But leading zeros do not count 028, 082, 088, 208, 280, 288, 802, 808, 820, 828, 880, 882 =9
Total = 2 + 5 + 9 = 16 possible numbers

 Jul 21, 2020
 #4
avatar+2445 
+2

Actually, the answer is 17.

 

1 digit possibilities: 0, 2, 8

2 digit possibilities: 28, 82, 20, 80, 88

3 digit possibilities: 208, 802, 288, 882, 808, 288, 280, 820

 

So, 3+5+9=17.

 

Is this correct?

 Jul 21, 2020
 #6
avatar+27660 
+1

What about   828 ?    880?      Hmmmmm....

 

   ( i do not think '0' counts)   ......

ElectricPavlov  Jul 21, 2020
edited by ElectricPavlov  Jul 21, 2020
edited by ElectricPavlov  Jul 21, 2020
 #7
avatar+2445 
+2

Sorry. I got the three digit possibilities wrong.

 

It's 288, 828, 288, 882, 288

 

Zero does count. It's less than 1,000, right?

CalTheGreat  Jul 21, 2020
 #5
avatar+392 
+1

That's correct! and nice explanation thanks :)

 Jul 21, 2020

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