A student council is made up of 6 seniors, 5 juniors, and 4 sophmores. How many ways can this student council select its president, vice-president, and treasurer? What is the probability that the officers will be either all seniors, or all juniors, or all sophmores?

For the first part of the question I have 15 nPr 3 = 2,730 ways they can be chosen, is this correct?

The second part gets a little hazy for me. I have the probability being... probability of all seniors + probability of all juniors + probability of all somphmores since the word OR was used. Maybe I am not reading the question right...

Then I broke it down as the senior probability equals (6/15)(5/14)(4/13)=

junior probability equals (5/15)(4/14)(3/13)=

sophmore probabilty eqauls (4/15)(3/14)(2/13)=

I feel like I need to divide something by the number of ways it can be done. What am I doing wrong???