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How many solutions (using only nonnegative integers) are there to the equation $$x_1+ x_2 + x_3 + x_4 + x_5 = 31\;?$$

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  • $\begingroup$ Where did you come across this problem, and how would you approach solving it? $\endgroup$ – Mike Pierce Mar 30 '16 at 23:44
  • $\begingroup$ Please see Stars and Bars (combinatorics, Wikipedia) or the many answers on MSE that discuss Stars and Bars. $\endgroup$ – André Nicolas Mar 30 '16 at 23:45