# Thread: How many 3 digit ...

1. ## How many 3 digit ...

How many 3 digit numbers less than 500 can we form using the digits 1,2,3,4,5,6,7
without REPETITION ?

starting from ones ---> (7)(6)(4) = 168

starting form hundreds ---> (4)(6)(5) = 120

Which answer is correct ? and WHY ??

2. Originally Posted by razemsoft21
How many 3 digit numbers less than 500 can we form using the digits 1,2,3,4,5,6,7
without REPETITION ?
starting form hundreds ---> (4)(6)(5) = 120
The number looks like $HTD$ where $H$ can be any one of $1,2,3,4$.
So how many choices do you now have for $T~?$
Finish it.

3. Originally Posted by Plato
The number looks like $HTD$ where $H$ can be any one of $1,2,3,4$.
So how many choices do you now have for $T~?$
Finish it.
OK , but why method 1 doesn't work (starting for ones) 7*6 and the take the hundreds which is 4 and get 168 numbers

4. Originally Posted by razemsoft21
OK , but why method 1 doesn't work (starting for ones) 7*6 and the take the hundreds which is 4 and get 168 numbers
It does not work because it is wrong.
The hundredth digit is restricted, so the other two are dependent on that choice.