Find the number of arrangements of the letter | vedclass

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(D) The word '$ALGEBRA$' consists of $7$ letters: $A, L, G, E, B, R, A$.The vowels are $A, E, A$ and the consonants are $L, G, B, R$.The positions of

Vedclass · Accepted Answer

$72$

Vedclass · Answer

(D) The word '$ALGEBRA$' consists of $7$ letters: $A, L, G, E, B, R, A$.The vowels are $A, E, A$ and the consonants are $L, G, B, R$.The positions of the letters are $1, 2, 3, 4, 5, 6, 7$.The vowels are at positions $1, 4, 7$ and the consonants are at positions $2, 3, 5, 6$.Since we must not alter the relative positions,the vowels must occupy the $3$ designated vowel positions and the consonants must occupy the $4$ designated consonant positions.The number of ways to arrange the vowels $(A, A, E)$ in $3$ places is $\frac{3!}{2!} = 3$.The number of ways to arrange the consonants $(L, G, B, R)$ in $4$ places is $4! = 24$.Total number of arrangements $= 3 	imes 24 = 72$.

Find the number of arrangements of the letters of the word '$ALGEBRA$' without altering the relative position of the vowels and the consonants.

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