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CBSE Class 11-science Answered

<div>How many words with or without meaning each with 2 vowels and 3 consonants can be formed from the letters of the word FRACTION?</div> <div> </div> <div>Find the number of arrangements of the letters of the word INTERMEDIATE</div> <div>In how many of these arrangements</div> <div>i) do the words start and end with the letter I</div> <div>ii) do all the E's always occur together</div>

Asked by ahuja8087 | 08 Jun, 2016, 12:35: AM

Expert Answer

left parenthesis 1 right parenthesis T h e r e space a r e space 5 space c o n s o n a n t s comma space F comma space R comma space C comma space T space a n d space N A n d space t h r e e space v o w e l s comma space A comma space I comma space O O u t space o f space 5 space c o n s o n a n t s space w e space n e e d space t o space s e l e c t space 3 space a n d space t h i s space c a n space b e space d o n e space i n space C presuperscript 5 subscript 3 space w a y s O u t space o f space 3 space v o w e l s space w e space n e e d space t o space s e l e c t space 2 space a n d space t h i s space c a n space b e space d o n e space i n space C presuperscript 3 subscript 2 space w a y s T h u s space comma space t h e r e space a r e space C presuperscript 5 subscript 3 cross times C presuperscript 3 subscript 2 space n u m b e r space o f space w a y s space i n space s e l e c t i n g space 3 space c o n s o n a n t s space a n d space 2 space v o w e l s. S i n c e space i n space a space w o r d space t h e r e space a r e space 3 space c o n s o n a n t s space a n d space 2 space v o w e l s comma space t h e r e space 5 space l e t t e r s space i n space a space g r o u p comma space w h i c h space t h e m s e l v e s space c a n b e space a r r a n g e d space i n space 5 factorial space w a y s. T h u s comma space i n space t o t a l space t h e r e space a r e space 5 factorial cross times open parentheses C presuperscript 5 subscript 3 cross times C presuperscript 3 subscript 2 close parentheses space n u m b e r space o f space w a y s space i n space s e l e c t i n g space 3 space c o n s o n a n t s space a n d space 2 space v o w e l s. open parentheses 2 close parentheses C o n s i d e r space t h e space w o r d space I N T E R M E D I A T E T h e r e space a r e space 12 space l e t t e r s space i n space t o t a l space o u t space o f space w h i c h space E space i s space r e p e a t i n g space 3 space t i m e s comma space I space i s space r e p e a t i n g space 2 space t i m e s space a n d space T space i s space r e p e a t i n g space 2 space t i m e s left parenthesis i right parenthesis A c c o r d i n g space t h e space q u e s t i o n space s t a t e m e n t comma space p o s i t i o n s space o f space 2 space I s space a r e space f i x e d. T h u s space t h e r e space a r e space 10 space l e t t e r s space o u t space o f space w h i c h space E space i s space r e p e a t i n g space 3 space t i m e s space a n d space T space i s space r e p e a t i n g space 2 space t i m e s T h u s comma space t o t a l space n u m b e r space o f space a r r a n g e m e n t s space equals fraction numerator 10 factorial over denominator 3 space factorial cross times 2 space factorial end fraction left parenthesis i i right parenthesis A c c o r d i n g space t o space t h e space q u e s t i o n space s t a t e m e n t comma space a l l space t h e space t h r e e space E s space s h o u l d space b e space t o g e t h e r. T h u s comma space apostrophe E E E apostrophe space c a n space b e space c o n s i d e r e d space a s space o n e space u n i t. T h u s space t h e space l e t t e r s space a r e space I comma space N comma space T comma space R comma space space M comma space D comma space I space A comma space T comma space apostrophe E E E apostrophe T h e r e space a r e space 10 space l e t t e r s space o u t space o f space w h i c h space space I space i s space r e p e a t i n g space 2 space t i m e s space a n d space T space i s space r e p e a t i n g space 2 space t i m e s T h u s comma space t o t a l space n u m b e r space o f space a r r a n g e m e n t s space equals fraction numerator 10 factorial over denominator 2 space factorial cross times 2 space factorial end fraction

Answered by Vimala | 08 Jun, 2016, 10:13: AM

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