Find the number of all possible different words into which the word INTERFERE can be converted by change of place of letters,if no two consonants must be together.


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Question Number 26480 by NECx last updated on 26/Dec/17

$F i n d t h e n u m b e r o f a l l p o s s i b l e$ $d i f f e r e n t w o r d s i n t o w h i c h t h e$ $w o r d I N T E R F E R E c a n b e$ $c o n v e r t e d b y c h a n g e o f p l a c e o f$ $l e t t e r s, i f n o t w o c o n s o n a n t s$ $m u s t b e t o g e t h e r .$
	Answered by mrW1 last updated on 26/Dec/17

	$T h e c o n s o n a n t s N T R F R m u s t b e$ $s e p a r a t e d b y t h e o t h e r 4 l e t t e r s .$ $X Y X Y X Y X Y X$ $Y = p o s i t i o n o f v o w e l s$ $X = p o s i t i o n o f t h e c o n s o n a n t s$ $T o a r r a n g e t h e 4 v o w e l s (I E E E) :$ $4 w a y s$ $T o a r r a n g e t h e 5 c o n s o n a n t s :$ $\frac{5!}{2!} = 5 \times 4 \times 3 = 60 w a y s$ $N u m b e r o f w o r d s :$ $4 \times 60 = 240$
	Commented by NECx last updated on 26/Dec/17

	$t h a n k s b o s s$
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