## anonymous one year ago The number of two-digit positive integers for which the units digit is not equal to the tens digit.

1. misty1212

HI!!

2. anonymous

hi misty =)

3. misty1212

my guess is $$81$$ reason as follows: you have nine choices for the tens place digit (it cannot be zero) then another 9 choices for the ones place (it can be zero, but it cannot be the tens digit)

4. misty1212

by the counting principle you get $$9\times 9=81$$

5. anonymous

ouuuuu niceeeee okay got it thanks!

6. misty1212

course i could be wrong maybe @geerky42 has a different answer

7. anonymous

it was right

8. geerky42

There are $$99-10+1 = 90$$ two digits numbers. Now exclude numbers where tens digit and unit digit are same; 11, 22, 33, 44, ..., 99 There are $$9$$ of them. So you have $$90-9 = \boxed{81}$$ So @misty1212 is correct.

9. anonymous

hey why do u exclude the 11, 22,33,44 etc.?????

10. misty1212

for which the units digit is not equal to the tens digit.

11. anonymous

but doesnt that just mean 10, 20, 30, 40 etc?

12. geerky42

No. "units digit is equal to the tens digit" means 11, 22, 33, etc. So here, we have "units digit is NOT equal to the tens digit", which means 10, 12, 13, ..., 20, 21, 23, ..., 31, 32, 34, ..., etc.

13. geerky42

We counted ALL two digits numbers, then we un-counted number where "units digit is equal to the tens digit"