SOLUTION: Find the number of way of arranging all the letters of the word TENNESSEE: a) the FIRST two letters must be EE b) the FIRST can NOT be EE

Examples:  EESENTNSE,  EEETSENSN, EENNSSTEE

So we just have to fill in the 7 letters after EE
from the 7 letters TENNESS in the blanks of:

E E _ _ _ _ _ _ _

Among the 7 letters of TENNESS there are 2 
indistinguishable E's, 2 indistinguishable
N's, and 2 indistinguishable S's, so

the answer is              

First we find all the distinguishable arrangements of 
the 9 letters TENNESSEE and then subtract the results of
part (a)

Among the 9 letters of TENNESSEE there are 4 
indistinguishable E's, 2 indistinguishable N's, and
2 indistinguishable S's, so the number of 
distinguishable arrangements of TENNESSEE is



But we must subtract all the distinguishable 
arrangements which begin with EE, so the answer
is 3780 - 630 = 3150

Edwin