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(D) The word $ALGEBRA$ has $7$ letters: $A, L, G, E, B, R, A$.The vowels are $A, E, A$ (at positions $1, 4, 7$).The consonants are $L, G, B, R$ (at po

Vedclass · Accepted Answer

$72$

Vedclass · Answer

(D) The word $ALGEBRA$ has $7$ letters: $A, L, G, E, B, R, A$.The vowels are $A, E, A$ (at positions $1, 4, 7$).The consonants are $L, G, B, R$ (at positions $2, 3, 5, 6$).To keep the relative positions fixed,we arrange the $3$ vowels in their $3$ positions and the $4$ consonants in their $4$ positions.Number of ways to arrange vowels $(A, E, A)$ $= \frac{3!}{2!} = 3$.Number of ways to arrange consonants $(L, G, B, R)$ $= 4! = 24$.Total number of permutations $= 3 	imes 24 = 72$.

How many permutations can be formed from the letters of the word $ALGEBRA$ without changing the relative positions of the vowels and consonants?

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