"ellipses" has consonants l,l,p,s,s and vowels e,i,e

First we find the number of ways positions can be chosen
to make sure the 5 consonants are together:

There are the following 4 ways of choosing positions 1 through 8
to be held by consonants and vowels.  There are these four with 
the 5 consonants together:
 
CCCCCVVV, VCCCCCVV, VVCCCCCV, and VVVCCCCC

For each of those 4 choices of positions to be held by 
consonants and vowels,

there are  = 30  ways to arrange the consonants since the
2 l's are indistinguishable and the two s's are indistinguishable,

and there are  = 3 ways to arrange the vowels since the 2 e's
are indistinguishable.

Answer 4×30×3 = 360 

Edwin