how many three digit numbers are there with no digit repeated
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
Let the 3 digit number be A B C
Then, there are 9 choices for digit A because it can be anything out of ( 1 , 2 , 3 , . . . , 9 ) ( 0 is not allowed as A because then number is not 3 digit)
Then, there are again 9 choices for digit B , because you can't take the digit which was chosen for A but you can take 0 this time, giving 9 choices,
Now, for C , you have 8 choices because 2 out of the total 1 0 digits have already been chosen.
Thus by the M u l t i p l i c a t i o n R u l e , there will be 9 × 9 × 8 = 6 4 8 numbers.