Marbles and Containers

Probability Level 3

I have 2016 identical marbles. I plan to distribute them equally into one or more identical containers. How many ways can this be done if I have an unlimited number of containers?


The answer is 36.

Samuel Job Espartero by Samuel Job Espartero , 21, Philippines

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1 solution

Efren Medallo
May 12, 2017

Note that 2016 = 2 5 ⋅ 3 2 ⋅ 7 2016 = 2^5 \cdot 3^2 \cdot 7 . We need to find the number of divisors of 2016 2016 , which is given by

( 5 + 1 ) ( 2 + 1 ) ( 1 + 1 ) = 6 ( 3 ) ( 2 ) = 36 (5+1)(2+1)(1+1) = 6(3)(2) = 36

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