How many 6-permutations of [15] have their digits listed in increasing order? (where [15] is the set of positive intergers <= 15)

I am thinking that this would be just $\displaystyle \left({15\atop 6}\right)$.

Consider 3-permutations of [5] in increasing order...

123 124 125 134 135 145 234 235 245 345 which has 10 different members which is $\displaystyle \left({5\atop 3}\right)$.

Would this be correct?