Question

which of the following gives the number of ways to make a 3-digit locker combination out of the digets 0-9 if the numbers are not repeated ​

Answer 1

It would be P(10,3).

Answer 2

720

Explanation:

The total digits in 0-9 are 10. To make a 3-digit locker combination, the digits should not be repeated.

There are 10 digits so any number out of 10 can be put in the first place of the combination.

So, ans=10

Now suppose 7 comes at first place and therefore (10-1) = 9 digits are remaining to be put at the second place.

So, ans=10*9

Assume 5 comes at the second place in the combination and therefore (9-1) = 8 digits are remaining to be put at the third place.

So, ans=10*9*8=720