WBJEE · Maths · Permutation Combination
The number of ways in which the letters of the word 'VERTICAL' can be arranged without changing the order of the vowels is
- A \(6 ! \times 3 !\)
- B \(\frac{8 !}{3}\)
- C \(6 ! \times 3\)
- D \(\frac{8 !}{3 !}\)
Answer & Solution
Correct Answer
(D) \(\frac{8 !}{3 !}\)
Step-by-step Solution
Detailed explanation
Hint : Vowels 'EIA' to be kept in order, so out of 8 places 3 places can be chosen in \({ }^8 \mathrm{C}_3\) ways. Remaining 5 letters can be arranged in 5 ! ways. \(\therefore\) Total number of ways \(={ }^8 \mathrm{C}_3 \times 5 !=\frac{8 !}{3 !}\)
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