Question

In how many ways can the letters of the word $BILASPUR$ be arranged so that three vowels may never be put together?

Answer 1

BILASPUR

Total combinations - vowels cone together

= vowels don't come together

$\Rightarrow$ Total combinations = 8!

vowels come together = $\left(iau\right)\left(b\right)\left(l\right)\left(s\right)\left(p\right)\left(r\right)$

$3!6!$

Ans $\Rightarrow 8!-3!6!=8\times 7\times 6!-3!6!$

$=6!(8\times 7-3\times 2)$

$=6!(56-6)$

$=720\times 50=3600$