How many $6$-permutations of $[15]$ have their digits listed in increasing order? $[15]$ is the set of first $15$ naturals. In my textbook permutation means a sequence without repetition. 
There are $15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10$ permutations. For each word like $123456$ there's a word like $654321$. So to remove the words of decreasing order we could probably divide $15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10$ by $2$. But there are also words that are neither of decreasing, nor of increasing order. I am stumped here. Some kind of hint and/or comment would be great. 

You only need to look at the number of ways you can choose $6$ elements out of $15$ -- the order is already imposed on you (once the elements are chosen, there is only one way you can order them).
