SOLUTION: In a city school during the admission to class XI, 18 students took English, 23 took Hindi and 24 students took Sanskrit. Of these, 13 took both Hindi and Sanskrit, 12 took both En
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Question 1181549: In a city school during the admission to class XI, 18 students took English, 23 took Hindi and 24 students took Sanskrit. Of these, 13 took both Hindi and Sanskrit, 12 took both English and Hindi and 11 took both English and Sanskrit. Due to the request made by the students, the school authorities decided that 6 students will be offered all the three languages. Kindly also provide the Venn digram
Based on the above information answer the following:
(i) The total number of students who took admission in class XI, is
(a) 35
(b) 30
(c) 33
(d) 45
(ii) How many students took Sanskrit but not Hindi?
(a) 6
(b) 19
(c) 11
(d) 9
(iii) How many students took exactly one of the three subjects?
(a) 25
(b) 11
(c) 20
(d) 21
(iv) How many students took exactly two of the three subjects?
(a) 11
(b) 21
(c) 8
(d) 18
(v) How many students took Hindi but not Sanskrit?
(a) 9
(b) 10
(c) 19
(d) 13
There are too many questions in the post, so I will answer the first question, ONLY.
Use the "inclusion-exclusion principle".
The number of students in the union is the sum of the students in three subsets (English, Hindi and Sanskrit)
separately MINUS numbers of elements in in-pair intersections PLUS the number of students in the triple
intersection (thus you have an "alternate sum", for clarity)
18 + 23 + 24 - 13 - 12 - 11 + 6 = 35.
ANSWER. 35 students took admission in class XI.
Solved.
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On inclusion-exclusion principle, see this Wikipedia article
