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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 Finance and Operations but not Marketing?
    Correct answer is '48'. 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.
    We have to maximize the number of students who chose both Finance and Operations as their specialization. We know that the number of students who chose Marketing will be greater than the number of students who opted for Finance and Operations as their specialization. This can be done as shown in the following Venn diagram.
    Thus, the maximum number of students who opted for Finance and Operations but not Marketing = 48
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    Most Upvoted Answer
    Read the below information carefully and answer the following question...
    Analysis:
    To solve this problem, we need to understand the given conditions and deduce the maximum possible values for each specialization.

    Given conditions:
    1. The number of students who opted for Marketing is more than the number of students who opted for Finance.
    2. The number of students who opted for Finance is more than the number of students who opted for Operations.
    3. The number of students who opted for Operations is more than the number of students who opted for exactly two of the three specializations.
    4. 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.
    5. At least one student opted for all three specializations.

    Deductions:
    Let's analyze each condition and deduce the maximum possible values for each specialization.

    1. The number of students who opted for Marketing is more than the number of students who opted for Finance.
    - This implies that the number of students who opted for Marketing (M) is greater than the number of students who opted for Finance (F).

    2. The number of students who opted for Finance is more than the number of students who opted for Operations.
    - This implies that the number of students who opted for Finance (F) is greater than the number of students who opted for Operations (O).

    3. The number of students who opted for Operations is more than the number of students who opted for exactly two of the three specializations.
    - This implies that the number of students who opted for Operations (O) is greater than the number of students who opted for exactly two specializations (T).

    4. 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.
    - This implies that the number of students who opted for exactly two specializations (T) is greater than the number of students who opted for all three specializations (A).

    5. At least one student opted for all three specializations.
    - This implies that the number of students who opted for all three specializations (A) is greater than or equal to 1.

    Maximum values:
    Based on the deductions, we can conclude the following maximum values for each specialization:

    - Maximum number of students who opted for Marketing (M) = 100 - A (As all students have to choose at least one specialization)
    - Maximum number of students who opted for Finance (F) = M - 1 (As the number of students who opted for Marketing is more than Finance)
    - Maximum number of students who opted for Operations (O) = F - 1 (As the number of students who opted for Finance is more than Operations)
    - Maximum number of students who opted for exactly two specializations (T) = O - 1 (As the number of students who opted for Operations is more than exactly two specializations)
    - Maximum number of students who opted for all three specializations (A) = At least 1

    Calculating the maximum number of students who opted for Finance and Operations but not Marketing:
    To calculate the maximum number of students who opted for Finance and Operations but not Marketing, we need to find the value of F - O. Let's substitute the maximum values we deduced:

    - Maximum number of students who opted for Finance and Operations = F - O
    - F = M - 1
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