Number of solutions of an inequality

Probability Level 4

Find the number of ordered 6-tuples of integers a1,a2,a3,a4,a5,a6a_1,a_2,a_3,a_4,a_5,a_6 satisfying

0a1a2a3a65.0 \leq a_{1} \leq a_{2} \leq a_{3} \leq \dots \leq a_{6} \leq 5.

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