SATHEE: Permutations And Combinations Question 291

Permutations And Combinations Question 291

Question: All the letters of the word ?EAMCET? are arranged in all possible ways. The number of such arrangements in which two vowels are not adjacent to each other is [EAMCET 1987; DEC 2000]

Options:

A) 360

B) 114

C) 72

D) 54

Show Answer

Answer:

Correct Answer: C

Solution:

First, we arrange 3 consonants in $ 3\ ! $ ways and then at four places (two places between them and two places on two sides) 3 vowels can be placed in $ ^{4}P_3\times \frac{1}{2\ !} $ ways. Hence the required number $ =3\ !\ {{\times }^{4}}P_3\times \frac{1}{2\ !}=72 $ .

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Permutations And Combinations Question 291

Question: All the letters of the word ?EAMCET? are arranged in all possible ways. The number of such arrangements in which two vowels are not adjacent to each other is [EAMCET 1987; DEC 2000]

Options:

Answer:

Solution:

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