+0

+1
94
7

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

Jul 20, 2020

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

Nice try! But that's incorrect

12 is wrong, too :(

Jul 21, 2020
edited by HelpBot  Jul 21, 2020
#3
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
+2

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
+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
+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
+1

That's correct! and nice explanation thanks :)

Jul 21, 2020