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Read the below information carefully and answer the following questions.
There are 100 students in a class. Each of the students has to opt for one or more of the three specializations among Finance, Operations and Marketing. The number of students who opted for Marketing is more than the number of students who opted for Finance which is more than the number of students who opted for Operations which is more than the number of students who opted for exactly two of the three specializations which is more than the number of students who opted for all three specializations. At least one student opted for all three specializations.
 
Q. What is the maximum number of students who opted for only Finance?
    Correct answer is '49'. Can you explain this answer?
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    Read the below information carefully and answer the following question...
    It is known that the total number of students is 100. We also know that the number of students who opted for Marketing is more than the number of students who opted for Finance which is more than the number of students who opted for Operations.
    The number of students who study study only finance cannot be 50. This is because in that case the number of people in only finance is 50 then there will be at least 51 people in finance (At least one person opted for all 3). Thus, marketing cannot be greater than finance in that case. Now let us consider the number of students in finance to be 49. In this case we can arrange the other people as shown in the venn diagram. None of the given condition is violated in the given diagram. Hence, at max 49 people can opt for only finance.
    Thus, the maximum number of students who opted for only Finance is 49
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    Read the below information carefully and answer the following question...
    Given Information:
    - There are 100 students in a class.
    - Each student can opt for one or more of the three specializations: Finance, Operations, and Marketing.
    - The number of students who opted for Marketing is more than the number of students who opted for Finance.
    - The number of students who opted for Finance is more than the number of students who opted for Operations.
    - The number of students who opted for Operations is more than the number of students who opted for exactly two of the three specializations.
    - The number of students who opted for exactly two of the three specializations is more than the number of students who opted for all three specializations.

    Objective:
    To find the maximum number of students who opted for only Finance.

    Assumptions:
    - At least one student opted for all three specializations.

    Step-by-Step Solution:

    Step 1: Finding the minimum number of students who opted for all three specializations.
    - Since at least one student opted for all three specializations, the minimum number of students who opted for all three specializations is 1.

    Step 2: Finding the minimum number of students who opted for exactly two of the three specializations.
    - Since the number of students who opted for exactly two of the three specializations is more than the number of students who opted for all three specializations, the minimum number of students who opted for exactly two of the three specializations is 2.

    Step 3: Finding the minimum number of students who opted for Operations.
    - Since the number of students who opted for Operations is more than the number of students who opted for exactly two of the three specializations, the minimum number of students who opted for Operations is 2 + 1 = 3.

    Step 4: Finding the minimum number of students who opted for Finance.
    - Since the number of students who opted for Finance is more than the number of students who opted for Operations, the minimum number of students who opted for Finance is 3 + 1 = 4.

    Step 5: Finding the minimum number of students who opted for Marketing.
    - Since the number of students who opted for Marketing is more than the number of students who opted for Finance, the minimum number of students who opted for Marketing is 4 + 1 = 5.

    Step 6: Finding the maximum number of students who opted for only Finance.
    - The total number of students in the class is 100.
    - The minimum number of students who opted for all three specializations is 1.
    - The minimum number of students who opted for exactly two of the three specializations is 2.
    - The minimum number of students who opted for Operations is 3.
    - The minimum number of students who opted for Finance is 4.
    - The minimum number of students who opted for Marketing is 5.
    - Therefore, the maximum number of students who opted for only Finance is the remaining number of students after considering all the other specializations: 100 - (1 + 2 + 3 + 5) = 100 - 11 = 89.

    Therefore, the maximum number of students who opted for only Finance is 89.
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