Answer:
65 candidates.
Step-by-step explanation:
From the above question, we have the following information
Total number of graduate students = n(B ∪ MP ∪ MC)
200 students
Number of students with bicycle = n(B) = 110
Number of students with MasterCard = n(MC) = 25
Number of students with Mobile phone = n(MP) = 130
Number of students with both bicycle and Master card = n ( B ∩ MC) = 50
Number of students with both Mastercard and Mobile phone = n ( MC ∩ MP) = 30
Number of students with both Bicycle and Mobile phone = n ( B ∩ MP) = 60
Number of students that had all three =
n ( B ∩ MP ∩ MC) = 10
Number of candidates that had none of the three = ( None of B ∩ MP ∩ MC)
Since this is a three element set, the formula is given as:
n(B ∪ MP ∪ MC) = n(B) + n ( MP) + n (MC) - n ( B ∩ MP) - n ( B ∩ MC) - n ( MC ∩ MP) + n (B ∩ MP ∩ MC) + ( None of B ∩ MP ∩ MC)
n(B ∪ MP ∪ MC) - ( None of B ∩ MP ∩ MC) = n(B) + n ( MP) + n (MC) - n ( B ∩ MP) - n ( B ∩ MC) - n ( MC ∩ MP) + n (B ∩ MP ∩ MC)
200 - ( None of B ∩ MP ∩ MC) = 110 + 25 + 130 - 60 - 50 -30 + 10
200 - ( None of B ∩ MP ∩ MC) = 110 + 25 + 130 + 10 - 60 - 50 - 30
= 200 - ( None of B ∩ MP ∩ MC) = 275 - 140
= 200 - ( None of B ∩ MP ∩ MC) = 135
( None of B ∩ MP ∩ MC) = 200 - 135
( None of B ∩ MP ∩ MC) = 65
Therefore, 65 candidates had none of the three
