Find the number of arrangements which can be made out of the letters of the word algebra, without altering the relative positions of vowels and consonants.
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Solution
⟹ Considering 3 bundles of letters, ′al′,′geb′,′ra′. Total arrangements of 3 bundles =3! The bundles can arrange internally in 2!,3!, and 2! ways. ∴ Total Number of ways =3!×2!×3!×2!2! Since ′a′ is twice ∴ Total no. of ways =72