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Question

In how many ways can the letters of the word FAILURE be arranged so that the consonants may occupy only odd positions?

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Solution

In the word FAILURE, there are 4 odd position for letters and 3 even positions.
Now we have 3 consonants and 4 places.
No. of ways to arrnage 3 consonant in 4 places =4P3=4×3×2=24 ways
No. of ways to occupy remaining 4 vowels =4!=24 ways
Total no. ways =24×24=576 ways

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