a word is formed with 3 vowels and 3 consonants without repetition . the probability the formation of words begining the letter z is?


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Question Number 82111 by john santu last updated on 18/Feb/20

$a w o r d i s f o r m e d w i t h 3 v o w e l s$ $a n d 3 c o n s o n a n t s w i t h o u t$ $r e p e t i t i o n . t h e p r o b a b i l i t y t h e$ $f o r m a t i o n o f w o r d s b e g i n i n g t h e$ $l e t t e r z i s ?$
Commented by john santu last updated on 18/Feb/20

$i^{'} g o t a n s w e r p = \frac{C_{2}^{20}}{6 \times C_{3}^{21}}$
Commented by mr W last updated on 18/Feb/20

$p = \frac{C_{2}^{20} C_{3}^{5} 5!}{C_{3}^{21} C_{3}^{5} 6!} = \frac{C_{2}^{20}}{6 C_{3}^{21}} = \frac{1}{42}$
Commented by jagoll last updated on 18/Feb/20

$n (S) = 6! C_{3}^{21} . C_{3}^{5}$ $n (A) = 5! C_{2}^{20} . C_{3}^{5}$ $p (A) = \frac{5! C_{2}^{21} . C_{3}^{5}}{6! C_{3}^{21} . C_{3}^{5}} = \frac{C_{2}^{21}}{6 . C_{3}^{21}}$
Commented by mr W last updated on 18/Feb/20

$6 i s c o r r e c t s i r!$
Commented by jagoll last updated on 18/Feb/20

$t h a n k y o u s i r$
Commented by john santu last updated on 18/Feb/20

$t h a n k y o u . i w r o t e i t w r o n g b e c a u s e$ $i n a h u r r y$
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