Question

How many even 4-digit numbers can be formed from the digits 1, 2, 3, 6, and 9 with no repetitions allowed? (Hint: Try filling the units place first.)

Answer 1

We need to find number of possible even 4-digit numbers that can be formed from the digits 1, 2, 3, 6, and 9 with no repetitions allowed:

Using the hint, we fill the units place first.

There are only 2 digits (2 and 6) that will make the 4-digit number an even number.(that is either the 4-digit number could end with 2 or it could end with 6). So possible ways to fill the units place = 2.

Then for next place, we have 4 digits left to fill that place since one digit is occupying units place. So possible ways to fill the next(tens) place = 4.

Similarly, for next place we are left with 3 digits that could fill that place (So possible ways to fill the place =3) and at last there would be only 2 digits left to fill the last place(So possible ways to fill the place = 2).

Therefore, total number would be:

Hence, number of possible even 4-digit numbers that can be formed from the digits 1, 2, 3, 6, and 9 with no repetitions allowed is 48