Find the number of different 8 letter words form e.d from the letter of the
word TIIANGIE is each word is to (i) begin with T (ii) end with E and begin
with T and end with E.
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Answer:
(1) all vowels occur together.
Total number of letter in DAUGHTER = 8
vowels in Daughter = A,U&,E
since all vowels occur together
Assume AUE as single object
So are word becomes AUE ,D, 4, H, T, 3
Now arranging 3 vowels
=
3
P
3
=
(3−3)!
3!
= 3!
= 6 way
arranging 6 letters
Numbers we need to arrange
5 + 1 = 6
=
6
P
6
= 6 !
= 720
Total No of average meets
=720×6
=7320
(1) all vowel do not occur together
total number of permutations - number of permutations all occur come together
total permutation =
8
P
8
= 40320
40320 - 4320 = 36000
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