How many nonnegative integer solutions are there to the equation: $x_1 + x_2 + x_3 + x_4 + x_5 = 40$ if we must satisfy $x_1 \le 20$?
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Using stars and bars, the number of solutions is given by $\binom{40+5-1}{5-1} = \binom{44}{4} = 163185$. Show more…
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