222000111555

Probability Level 4

A "triplete anual" is formed by natural numbers a , b , c , d a,b,c,d , in order, such that a + b + c + d = N a+b+c+d= N and N N is the actual year . For 2015 2015 , how many "tripletes anuales" there ?


The answer is 1359502364.

Paola Ramírez by Paola Ramírez , 24, Mexico

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1 solution

Paola Ramírez
Jan 6, 2015

Each pigeonhole has at least one unit, so 2011 2011 unities have been distributed in 4 4 pigeonholes. This can do it of ( 2014 3 ) \binom {2014}{3} ways = 1359502364 \boxed{1359502364}

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What do you mean by "natural numbers in order"?

Firstly, is 0 considered a natrual number? Please use "non-negative integer" and "positive integer" for clarity.

Secondly, what does "in order mean"? Is 1, 1, 1, 2012 in order? What about 1, 2012, 1, 1 is that in order?

Also, please avoid using the word "pigeonhole" unless you intend to talk about the pigeonhole principle. What I think you are referring to is stars and bars/stripes instead.

Calvin Lin Staff - 6 years, 5 months ago

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The order is important, not it is the same 1 , 1 , 2 , 2011 1,1,2,2011 than 2 , 1 , 1 , 2011 2,1,1, 2011 .

Sorry, I don't find it a good word for "casilla"

Paola Ramírez - 6 years, 5 months ago

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