Question
The number of ways of arranging letters of the word HAVANA so that V and N do not appear together is
BITSAT
Mathematics
Permutation Combination
2022
BITSAT 2022
BITSAT Mathematics Question (2022) — Solution
Options
- A. 40
- B. 60
- C. 80
- D. 100
Answer
C. 80
Step-by-step solution
We can arrange the letters H , A , A , A in 4 ! 3 ! =4 ways. If one possible arrangement is X X X X Then, we can arrange V , N at any of the two places marked with O in the following arrangement O O O O O Thus, we can arrange V and N in ^5 P_2=20 ways. Thus, the number of ways in which letters can be arranged is 4 20=80
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