Find-the-probability-that-a-student-arranging-the-letters-of-the-word-MATHEMATICS-will-make-all-the-vowels-be-together-in-any-arrangement-he-or-she-does-

Question Number 56025 by pieroo last updated on 08/Mar/19

Find the probability that a student

arranging the letters of the word

MATHEMATICS will make all the

vowels be together in any arrangement

he or she does .

Answered by tanmay.chaudhury50@gmail.com last updated on 08/Mar/19

A = 2 C = 1 E = 1 H = 1 I = 1 M = 2 S = 1 T = 2

(A A E I) C H M M S T T

(\frac{8!}{2! \times 2!}) \times \frac{4!}{2!} \to i t i s t h e a n s w e r

\frac{8 \times 7 \times 6 \times 5 \times 3 \times 2}{1} \times \frac{4 \times 3}{1} = 20160 \times 6 = 120960

d i s c u s s i o n

a s s u m e d v o w e l A A E I a r e F a b i q u i c k e d

p e r m u t a t i o n f o r A A E I

i s = \frac{4}{2!} d e n o m i n a t o r 2! f o r t w o A

p e r m u t a t i o n f o r (A A E I) C H M M S T T

\frac{8!}{2! \times 2!} \to d e n o m i n a t o r 2! f o r t w o (02) M

a n i t h e r 2! f o r t w o T

s o a n s w e r = \frac{8!}{2! 2!} \times \frac{4!}{2!}

y e s i f o r g o t t o f i n d p r o b a b l i t y \dots M r W s i r d o n e i t

p l s c h e c k \dots

Answered by mr W last updated on 08/Mar/19

A A E I = 4 l e t t e r s

M M T T H C S = 7 l e t t e r s

p = \frac{\frac{8!}{2! 2!} \times \frac{4!}{2!}}{\frac{11!}{2! 2! 2!}} = \frac{8! 4!}{11!} = \frac{4}{165} \approx 2 . 4 %

Commented by pieroo last updated on 08/Mar/19

Thanks sir,

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