Question

The total number of arrangements which can be made out of the letters of the word $"Algebra"$ without altering the relative positions of vowels and consonants is

• A. $\frac{7!}{2!}$
• B. $\frac{7!}{2!5!}$
• C. $4!3!$
• D. $\frac{4!3!}{2}$

Answer 1

The correct option is D $\frac{4!3!}{2}$

The four consonants all different can be arranged in $2nd,3rd,5th$ and $6th$ (four) places in $4!=24$ ways and three vowels $A,E,A$ out of which two are alike can be arranged in $1st,4th$ and $7th$ positions in $\left(\frac{3!}{2!}\right)=3$ ways.

Hence, the total number of ways is $24\times 3=72.$