Hi student,

Another way of thinking about it :

Those wearing both are included among those wearing socks and those wearing shoes.

So we can add another 6 to the total number of people such that we 'double count' them.

24 + 6 = 30

Now it's as good as saying the shoe wearing people and socks wearing people do not overlap, as though as they are entirely separate groups of people.


Barefooted people
= 30 - 12 - 8
= 10


Or

24 - 12 - 8 = 4

But we have double counted those who wear both and subtracted too much. We need to add 6 back.

4 + 6 = 10

Or we can also calculate shoe-only people and socks-only people first.

12 - 6 = 6 (shoe only)
8 - 6 = 2 (socks only)

Barefooted

= Total - shoe only - socks only - both

= 24 - 6 - 2 - 6
= 10



This is the same as :

Total - shoe only - socks(only and both included)

= 24 - 6 - 8
= 10

Or

Total - shoe (only and both included) - socks only

= 24 - 12 - 2
= 10

Ah... This is more visualize with @J's explanation.
Thank you again for your time. :)