Ho many three digit numbers have exactly two repeated digits?

I found 270 is it right?

let x be the repeated number we have three ways

xx_ 9*10 numbers= 90
_xx 9*10=90
x_x 9*10 = 90

so 90*3= 270 three digit numbers . Is this right?

Question

Ho many three digit numbers have exactly  two repeated digits?

I found 270 is it right?

let x be the repeated number we have three ways

xx_ 9*10 numbers= 90 
_xx  9*10=90
x_x 9*10 = 90

so 90*3= 270  three digit numbers  . Is this right?

reemii · Answer

those numbers start at 100 and end at 999. (first digit can't be 0 !)

other way of counting:
for each starting number D, you can either repeat it or choose another digit that will be 'double'.
D-D-E or D-E-E, or D-E-D. Therefore,
"For each of the 9 possible choices for D, there are 3×9 ways to continue the number."
I get 9×9×3.

reemii · Answer

243

reemii · Answer

the 27 other numbers are the one starting wth 0. you just overlooked this.

anonymous · Answer

No I think I considered that ,

so for example for XX_  the repeated x can be from 1 to 9  and the last number can be from 0 to 10 therefore
9*10 =90 3 digit number that look like 220,221,771 etc.

then for _XX (e.g 577)  the first digit can be from 1 to 9  and the doubled digit can be from 0 to 10 . so 9*10 = 90   . 100 , 111,122........900,911

the same for X_X , X can be from 1 to 9 and the middle can be 0 to 9  so we have 9*10 =90

anonymous · Answer

@reemii

reemii · Answer

you're not allowed to choose a _ digit that is already chosen as X.
if you choose X=2, you can't choose 2 for the _, so you have only 9 choices.

anonymous · Answer

Oh my god , yes you are right. Thanks !!

reemii · Answer

np