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

HelpBot 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.

ElectricPavlov Jul 20, 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

Guest Jul 21, 2020

#4**+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?

CalTheGreat Jul 21, 2020

#6

#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