Question

Prove that the total number of arrangement which can can be out of the letters of the word ALGEBRA without altering the relative position of vowels and consonants is $\frac{4!3!}{2}=72$.

Answer 1

The four consonants all different can be arranged in the four places in $4!=24$ ways and have three vowels $A,E,A$ out of which two are alike can be arranged in $\frac{3!}{2!}=3$ ways.

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