Question

The number of arrangements which can be made out of the letters of the word " ALGEBRA" so that no two vowels together is $360\lambda$ then $\lambda$ = __

Answer 1

$ALGEBRAVowels\Rightarrow A,F,A$

First we arrange consonent.

no.of ways$\Rightarrow 4!2)24$

now in the $5$ gaps between $4$ consonent we arrange $3$ vowels.

No. of ways ${\Rightarrow }^5{C}_3\times \frac{3!}{2!}\Rightarrow 10\times 3\Rightarrow 30$

$\therefore$ Total no. of words $=24\times 30=720-360\lambda$

$\Rightarrow \lambda =2$