In a certain college of the 100 students, 60% students took Finance course, 45% took Marketing course and 45 students took Operation Management course. If 10 students took all the courses and 10 students none of the three courses, how many students took exactly 2 of these 3 courses?

Question

Satt Academy · Accepted Answer

Here, to solve the problem, we need to use some laws from the primary concept of sets.

Let, n(F) = 60; n(M) = 45 n(Om)=45; n(T) = 100

All courses taken, n(F $\cap$ M $\cap$ Om )=10

None taken, n(F $\cup$ M $\cup$ Om )^ =10

We know, z(F $\cup$ M $\cup$ Om )=n(T)-n(F $\cup$ M $\cup$ Om)^

= n(F $\cup$ M $\cup$ Om)= 100 - 10 = 90

= So, we can write, n (F $\cup$ M $\cup$ Om)

= n(F)+n(M)+n(Om)-n(F $\cap$ M)-n(M $\cap$ Om)-n(Om $\cap$ F)+n(F $\cap$ M $\cap$ Om)

= 90=60+45+45-{n(F $\cap$ M)+n(M $\cap$ Om)+n(Om $\cap$ F}+10

=90=160-ln(F $\cap$ M)+n(M $\cap$ Om )+n(Om $\cap$ F)

$∴$ n(F $\cap$ M)+n(M $\cap$ Om )+n(Om $\cap$ F)=70

$∴$ The number of students who took 2 of these 3 courses is

=70-3 $\times$ (F $\cap$ M $\cap$ Om)= 70 - (3 $\times$ 10) = 70 - 30 = 40

In a certain college of the 100 students, 60% students took Finance course, 45% took Marketing course and 45 students took Operation Management course. If 10 students took all the courses and 10 students none of the three courses, how many students took exactly 2 of these 3 courses?
(Set)

Question:
In a certain college of the 100 students, 60% students took Finance course, 45% took Marketing course and 45 students took Operation Management course. If 10 students took all the courses and 10 students none of the three courses, how many students took exactly 2 of these 3 courses?
(Set)

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In a certain college of the 100 students, 60% students took Finance course, 45% took Marketing course and 45 students took Operation Management course. If 10 students took all the courses and 10 students none of the three courses, how many students took exactly 2 of these 3 courses? (Set)

Question: In a certain college of the 100 students, 60% students took Finance course, 45% took Marketing course and 45 students took Operation Management course. If 10 students took all the courses and 10 students none of the three courses, how many students took exactly 2 of these 3 courses? (Set)

গণিত

Related Question

Promotion

In a certain college of the 100 students, 60% students took Finance course, 45% took Marketing course and 45 students took Operation Management course. If 10 students took all the courses and 10 students none of the three courses, how many students took exactly 2 of these 3 courses?
(Set)

Question:
In a certain college of the 100 students, 60% students took Finance course, 45% took Marketing course and 45 students took Operation Management course. If 10 students took all the courses and 10 students none of the three courses, how many students took exactly 2 of these 3 courses?
(Set)