1. ## 6-permutations of [15]

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 $\left({15\atop 6}\right)$.

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 $\left({5\atop 3}\right)$.

Would this be correct?

2. Originally Posted by oldguynewstudent
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 $\left({15\atop 6}\right)$.

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 $\left({5\atop 3}\right)$.
Your example of 3,[5] is correct.
BUT consider {1,15,2,12,10,5} cannot be arranged having their digits listed in increasing order.
I would think that the answer is $\binom{9}{6}$.

Now I may have completely missread "their digits listed in increasing order".

3. Originally Posted by Plato
Your example of 3,[5] is correct.
BUT consider {1,15,2,12,10,5} cannot be arranged having their digits listed in increasing order.
I would think that the answer is $\binom{9}{6}$.

Now I may have completely missread "their digits listed in increasing order".
Thank you for pointing out this ambiguity. This is a first printing of the text.

The Hint in the back of the text says:

Once you know which six numbers are in the permutations, how many ways are there to put them in increasing order?

As always you are a gentleman and a scholar! Thank you again.

4. Originally Posted by oldguynewstudent
Once you know which six numbers are in the permutations, how many ways are there to put them in increasing order?
In that case it is $\binom{15}{6}$.