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Greatest value of nCr for a given n

This type of question, asked 2 times: 10 May 2024 S2, 13 May 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    10 May 2024 S2

    135
    The value of 10Cr11Cr\dfrac{^{10}C_r}{^{11}C_r}, when both the numerator and denominator are at their greatest values, is

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  2. Question 2

    13 May 2026 S2

    58
    The sum of the greatest values of 15Cr{}^{15}C_r and 12Cr{}^{12}C_r is equal to

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