In an arrangement of the word VIOLENT, find the chances that the vowels I, O, E occupy the odd positions.


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Question Number 82130 by TawaTawa last updated on 18/Feb/20

$In an arrangement of the word VIOLENT, find the chances$ $that the vowels I, O, E occupy the odd positions .$
Commented by mr W last updated on 18/Feb/20

$w e h a v e 4 o d d p o s i t i o n s : 1, 3, 5, 7$ $w e h a v e 3 e v e n p o s i t i o n s : 2, 4, 6$ $w e h a v e 3 v o w e l s : I, O, E$ $w e h a v e 4 c o n s o n a n t s : V, L, N, T$ $a s s u m e w e h a v e 4 v o l w e l s : I, O, E, A .$ $t o a r r a n g e t h e s e 4 v o l w e l s i n t h e 4$ $o d d p o s i t i o n s t h e r e a r e 4! w a y s . b u t$ $t h e A i s a f a k e, s h o u l d b e r e p l a c e d$ $w i t h o n e o f t h e 4 c o n s o n a n t s, t h e r e$ $a r e 4 p o s s i b i l i t i e s . t o a r r a n g e t h e$ $3 r e m a i n i n g c o n s o n a n t s i n t h e 3$ $e v e n p o s i t i o n s t h e r e a r e 3! w a y s . s o$ $w e h a v e t o t a l l y 4! \times 4 \times 3! w a y s t o$ $b u i l d w o r d s w i t h v o l w e l s i n o d d$ $p o s i t i o n s .$
Commented by TawaTawa last updated on 19/Feb/20

$Ohh, i understand very well now sir . God bless you .$
Commented by john santu last updated on 18/Feb/20

$p = \frac{4 \times 3! \times 4!}{7!} = \frac{4 \times 6}{7 \times 6 \times 5} = \frac{4}{35}$
Commented by TawaTawa last updated on 18/Feb/20

$God bless you sir .$
Commented by TawaTawa last updated on 18/Feb/20

$Sir, i {don}^{'} t understand how you got : 4 \times 3! \times 4!$
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