Problematic Mathematics, or Simple Logic?

Probability Level 2

You have to choose 40 numbers, each having a value less than 100.

How many combinations can be made such that the average of these 40 numbers is greater than 120?

( 40 10 ) \left( \begin{matrix} 40 \\ 10 \end{matrix} \right) ( 40 25 ) \left( \begin{matrix} 40 \\ 25 \end{matrix} \right) 40 ( 40 40 ) \left( \begin{matrix} 40 \\ 40 \end{matrix} \right) None of These 124 59 120

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Vaibhav Prasad by Vaibhav Prasad , 21, India

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1 solution

Luca Ferrigno
Jul 11, 2015

The arithmetic mean is always less or equal than the maximum value, so the biggest number has to be greater or equal than 120, but all the numbers are less than 100 so there are no solutions

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