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