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Q.
The total number of words which can be formed using all the letters of the word "AKSHI" if each word begins with vowel or terminates with vowel -
Permutations and Combinations
Solution:
Total possible words - words do not begin or terminate with vowel
Total words $=5 !=120$
Words which do not begin and terminate with vowel $=3 \,\,\, 3 \,\,\, 2 \,\,\, 1 \,\,\, 2=36$
Desired words : $180-36=84$
II-Method $\rightarrow$ words which begin with vowel $( A / l )=4 ! 2=48$ ways $\rightarrow$ say $= n ( A )$
Similarly words terminating with vowel
$=4 ! 2=48 \text { ways } \rightarrow \text { say }=n(B)$
Now exclude words which begin as well as terminates with vowel
$2\,\,\, 3\,\,\,2\,\,\,1\,\,\,1$ ways $\rightarrow n ( A \cap B )$
Desired number of words :-
$48+48-12=84$ ways
$(\because n(A \cup B)=n(A)+n(B)-n(A \cap B))$