Problem#20

Probability Level 3

A child had to calculate (n+k13)\dbinom{n+k-1}{3} but instead he calculated (n+k4)\dbinom{n+k}{4}. Interestingly both the answers were same. What is the maximum possible value of (n+4k)×(k+3k+1)\dbinom{n+4}{k}\times\dbinom{k+3}{k+1}. You may use a calculator for a final step. Given nn and kk are whole numbers.

This problem is a part of the series <One minute problems>

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