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  4. At a certain conference of 100 people, there are 29 Indian women and 23 Indian men. Of these Indian people 4 are doctors and 24 are either men or doctors. There are no foreign doctors. How many foreigners and women doctors are attending the conference?

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Q. At a certain conference of 100 people, there are 29 Indian women and 23 Indian men. Of these Indian people 4 are doctors and 24 are either men or doctors. There are no foreign doctors. How many foreigners and women doctors are attending the conference?

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Solution:

See the following Venn diagram
$n (I) = 29 + 23 = 52$
$n (F) = 100 - 52 = 48$
$n(M \cup D) = n(M) + n(D) - n(M\cap D)$
$24 = 23+ 4 - n(M\cap D)$
$\therefore n(M\cap D) = 3$
$\therefore W \cap D) = 4 -3 = 1$

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