Hello, ramdrop!

There are only *three* circles in the Venn diagram!

Anything outside the Male circle is a female.

Contruct the Venn diagram and insert the known quanatities and the

. . It looks like this . . .

Code:

*---------------------------*
| |
| *-----------* |
| | A | |
| | 5 *-------+---* |
| | | 6-x | B | |
| *---+---+---* | | |
| | | x | 2 | 3 | | |
| | *---+---+---* | |
| | | | 4+x | |
| | 7-x *---+-------* |
| | M | |
| *-----------* |
| 3 |
*---------------------------*

Add the quantities inside the three cicles:

. .

Since there are 30 patients on the ward,

. . there are 3 patients outside the three circles.

These are patients who are not male, are not 50 or older,

. . and do not have back problems.

These are *exactly* the patients the problem asked for!

. .