1. ## Is the answer provided wrong!?

Calculate the number of even numbers between 5000 and 7000 which can be formed from the digits 1,5,6 and 8 if repetitions are allowed.
I tried working on this question a few times and came to 48 but, the answer given is 60. Can anyone help me??? Thank you!

2. Hello cyt91
Originally Posted by cyt91
Calculate the number of even numbers between 5000 and 7000 which can be formed from the digits 1,5,6 and 8 if repetitions are allowed.
I tried working on this question a few times and came to 48 but, the answer given is 60. Can anyone help me??? Thank you!
I don't get either of these answers; I reckon it's 64. As follows:
The first digit is 5 or 6. So there are $2$ choices here.

The second and third digits can be any one of $4$; so that's $4^2$ choices.

The final digit must be 6 or 8: $2$ choices.
So the total number of choices, and hence the total number of numbers is:
$2\times4^2\times2=64$

3. Originally Posted by cyt91
Calculate the number of even numbers between 5000 and 7000 which can be formed from the digits 1,5,6 and 8 if repetitions are allowed.
I tried working on this question a few times and came to 48 but, the answer given is 60. Can anyone help me??? Thank you!
I'm getting 64

5--6 in the middle both equal........ 4 choices
5--6 in the middle both different... .4(3)=12 choices
5--8 in the middle both equal.........4
5--8 in the middle both different.....12
6--6 in the middle both equal.........4
6--6 in the middle both different.....12
6--8 in the middle both equal..........4
6--8 in the middle both different.....12

4. Thanks a lot. I've worked it out again. It is 64. Appreciate this!