4-permutations of [10]

Oct 2009
St. Louis Area
How many 4-permutations of [10] have maximum element equal to 6? How many have maximum element at most 6?

First part we have xxx6 which gives which gives \(\displaystyle \left(5\right)_{3}\)and since the 6 can appear in 4 different places the answer would be \(\displaystyle 4*\left(5\right)_{3}\).

The second part would be \(\displaystyle \left(6\right)_{4}\).

Is this correct?