A school awarded 42 medals in hockey 18 in basketball and 23 in cricket.If these medals were bagged by a total of 65 students and only 4 students got medals in all three sports,how many students recieved medals in exactly two out of three sports
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Answer: No. of students who got medal in two out of three sports is 22
Step-by-step explanation:
No. of students got medal in Hockey = 42
No. of students got medal in Basketball = 18
No. of students got medal in Cricket = 23
No. of students who got medal in all the three sports = 4
Total no. of students who got medal = 65
n(HUBUC) = n(H) + n(B) + n(C) - n(H∩B) - n(B∩C) - n(C∩H) + n(H∩B∩C)
65 = 42 + 18 + 23 - [ n(H∩B) + n(B∩C) +n(C∩H)] + 4
65 = 87 - [n(H∩B) + n(B∩C) +n(C∩H)]
[n(H∩B) + n(B∩C) +n(C∩H)] = 22
Therefore, no. of students who got medal in two out of three sports is 22
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