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How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?

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प्रश्न

How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?

योग
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उत्तर

ARTICLE

Vowels A, I, E = 3

Total number of places = 7

1 2 3 4 5 6 7

Number of even places = 3

3 Vowels can occupy 3 places in 3! = 3 × 2 × 1 = 6 ways

Then the remaining 4 letters can be arranged in 4! ways

So total number of arrangement = 3! × 4! = 6 × 24 = 144 ways

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अध्याय 4: Combinatorics and Mathematical Induction - Exercise 4.2 [पृष्ठ १७८]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
अध्याय 4 Combinatorics and Mathematical Induction
Exercise 4.2 | Q 7 | पृष्ठ १७८

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