Among 50 applicants for an MBA program, 28 have at least 2 degrees, 2

Solution

• The universal set is the people, who applied for an MBA program.
• Among them,

o Set A is the people who have atleast 2 degrees, and
o Set B is the people who have work experience
o D is the people who do not have atleast 2 degrees and work experience

• We are told that the total number of applicants are 50
• Among them,

o 28 applicants have atleast 2 degrees
o 20 applicants have work experience, and
o 12 applicants have less than 2 degrees and no work experience
• And we need to find out the number of applicants with work experience, who have atleast 2 degrees

• In this question, we do not know whether all the 50 applicants have either work experience or atleast 2 degrees.
• So, we cannot say that n(U) = n(A or B)
• Thus,

o n(U) = n(A or B) + n(D) = a + b + c + d = 50, where D is the number of people, who do not have either of them ………. (1)
o We are given that, n(A) = a + c = 28, ……………. (2)
o n(B) = b + c = 20, and ……………. (3)
o n(D) = d = 12 …………………. (4)
• And we are asked to find out the number of applicants, who have atleast 2 degrees, with work experience, which is n(A & B) = c

• (a + c) + (b + c) + d – (a + b + c + d) = 28 + 20 + 12 – 50
• Implies, c = 10