Permutation and CombinationMedium
Question
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 -
Options
A.84
B.12
C.48
D.60
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 → words which begin with vowel
(A/I) = 4! × 2 = 48 ways → say = n (A)
Similarly words terminating with vowel
- 4! × 2 = 48 ways → say = n(B)
Now exclude words which begin as well as terminates with vowel
2 × 3 × 2 × 1 × 1 = 12 ways → n (A ∩ B)
Desired number of words :-
48 + 48 - 12 = 84 ways
(∵ n(A υ B) = n(A) + n(B) - n (A ∩ B))
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 → words which begin with vowel
(A/I) = 4! × 2 = 48 ways → say = n (A)
Similarly words terminating with vowel
- 4! × 2 = 48 ways → say = n(B)
Now exclude words which begin as well as terminates with vowel
2 × 3 × 2 × 1 × 1 = 12 ways → n (A ∩ B)
Desired number of words :-
48 + 48 - 12 = 84 ways
(∵ n(A υ B) = n(A) + n(B) - n (A ∩ B))
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