6. How many ordered 5-tuples $(a, b, c, d, e)$ of integers satisfy $10<a<b<c<d<e<20$ ?
Answer: 126
Solution: We simply need to choose which five of the integers $11,12, \ldots, 19$ will comprise the 5 -tuple. Once the integers are chosen, there is only one way to assign them as $a, b, c, d, e$ to satisfy the given inequalities. Thus, there are $\binom{9}{5}=126$ possible 5 -tuples.