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?

(In reply to

Answer by K Sengupta)

Let us represent writing, design and programming respectively by a, b and c.

Let us denote union and intersection respectively by (+) and (*).

Then, in terms of the inclusion-exclusion principle, we must have:

N(a+b+c) = N(a) + N(b) + N(c) + N(a*b) + N(b*c) + N(c*a) - N(a*b*c) .......(i)

Let, N(a*b*c) = t (say)

Then, by the given conditions, we have:

N(a+b+c) = 30

N(a) = 18

N(b) = 20

N(c) = 23

N(a*b) = 6+t

N(b*c) = 7+t

N(c*a) = 4+t

Acordingly, in terms of (i), we obtain:

30 = 18+20+23 - (6+t) - (7+t) - (4+t) + t

-> 2t = 14

-> t = 7

Consequently, the required number of interviews is 7.

*Edited on ***December 9, 2008, 7:00 am**