Among the 120 students of a class, numbered 1 to 120, all even numbered students opt for Bangla, whose numbers are divisible by 5 opt for English and those numb

Among the 120 students of a class, numbered 1 to 120, all even numbered students opt for Bangla, whose numbers are divisible by 5 opt for English and those numbers are divisible by 7 opt for Math. How many opt for none of these three subjects?

Among the 120 students of a class, numbered 1 to 120, all even numbered students opt for Bangla, whose numbers are divisible by 5 opt for English and those numbers are divisible by 7 opt for Math. How many opt for none of these three subjects? ?

Created: 1 week ago | Updated: 1 week ago | Created By:

Imran Ahmed

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Best Answer Explained in Below-:

Here, Number of even numbered students, n(B) = 120/2 = 60 Number of numbers divisible by 5, n(E) = 120/5 = 24 Number of numbers divisible by 7, n(M) = 120/7 ≈17 Number of even numbers divisible by 5, n(BꓵE) = 24/2 = 12 Number of numbers divisible by both 5 & 7, n(EꓵM) = 3 Number of even numbers divisible by 7, n(BꓵM) = 17/2 ≈ 8 Number of even numbers divisible by both 5 & 7, n(BꓵEꓵM) = 1 Number of students opting for atleast one of the subjects = n(BUEUM) n(BUEUM) = n(B) + n(E) + n(M) - n(BꓵE) - n(EꓵM) - n(BꓵM) + n(BꓵEꓵM) = 60 + 24 + 17 - 12 - 3 - 8 + 1 = 79 Students opting for none of the subjects, n(BUEUM)' = 120 - n(BUEUM) = 120 - 79 = 41.

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