A job opening for a Webmaster has three desirable skills: writing, design, and programming. Of the received applications, 30 have at least one of these skills: 18 know design, 20 can write well, and 23 have programming ability. There are 6 with writing and design skills only, 7 with just writing and programming, and 4 who can design and program but can't write. Only those with all three skills are interviewed. How many interviews are there?

Easy inclusion-exclusion problem.

If you add up 18, 20 and 23 (to get 61), you've double counted all the people with exactly 2 skills (6 + 7 + 4 = 17 people). So if you subtract off those who've been double counted (giving you 44), you're left with the total (30 people) plus two times those who've got all three (who were triple-counted). Therefore, 7 people had all three desirable skills and were interviewed.

Anyway, wasn't this your homework?

Posted by terabyte on 2006-07-06 18:34:22