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The number of arrangements that can be formed out of 'LOGARITH

Question

The number of arrangements that can be formed out of 'LOGARITHM' so that no two vowels come together is

6!^{7} P_{3}

6! 7!

6! 3!

7! 3!

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The number of arrangements that can be formed out of 'LOGARITHM' so that no two vowels come together is

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Text solutionVerified

for no 2 vowels to appear together, we can place vowels in spaces

between consonants such as

⊻ C ⊻ C ⊻ C ⊻ C ⊻ C ⊻ C ⊻

Now, 6 constants can be placed in 6 ! ways (L, G, R, T, H, M)

7 spaces can be filled with 3 vowels (O, A, I) in

^{7} P_{3}

ways

Total no of arrangements =

6!^{7} P_{3}

∴

Option A is correct.

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Question Text	The number of arrangements that can be formed out of 'LOGARITHM' so that no two vowels come together is
Answer Type	Text solution:1
Upvotes	151