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CBSE Class 11-science Answered

<div>Find the number of different 8 letter words formed from the letters of the word'TRIANGLE' IF each word is to</div> <div>1.have no two vawels together</div> <div>2.have both consonants and vowels together</div> <div>3.have the relative position of the vowels and the consonants unaltered.</div>
Asked by krishnapriya20 | 07 Dec, 2015, 10:37: PM
Expert Answer
C o n s i d e r space t h e space w o r d comma space " T R I A N G L E " T h e r e space a r e space 8 space l e t t e r s space i n space t h e space w o r d space " T R I A N G L E " O u t space o f space t h e space 8 space l e t t e r s space i n space t h e space g i v e n space w o r d comma space v o w e l s space a r e space " I " comma space " A " space a n d space " E " S o space t h e space n u m b e r space o f space c o n s o n a n t s space i s space 5 space a n d space t h e y space a r e comma space " T " comma space " R " comma space " N " comma space " G " space a n d space " L "  1. S i n c e space n o space v o w e l s space s h o u l d space b e space p l a c e d space t o g e t h e r comma space l e t space u s space w r i t e space t h e space p o s i t i o n s space o f space t h e space c o n s o n a n t s space a s space f o l l o w s colon _ C _ C _ C _ C _ C _ 5 space c o n s o n a n t s space c a n space b e space p l a c e d space i n space 5 factorial space w a y s. 3 space v o w e l s space c a n space b e space p l a c e d space i n space 6 space p o s i t i o n s space i n space C presuperscript 6 subscript 3 space w a y s. T h u s space b y space t h e space f u n d a m e n t a l space p r i n c i p l e space o f space c o u n t i n g comma space t h e space t o t a l space n u m b e r space o f space w a y s space i n space w h i c h space t h e space w o r d space " T R I A N G L E " c a n space b e space f o r m e d space w i t h space n o space v o w e l s space t o g e t h e r equals C presuperscript 6 subscript 3 cross times 5 factorial space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 6 cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 over denominator 1 cross times 2 cross times 3 end fraction cross times 1 cross times 2 cross times 3 cross times 4 cross times 5 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 6 cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 cross times 4 cross times 5 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 14400  2. W e space n e e d space t o space f i n d space t h e space n u m b e r space o f space w o r d s space t h a t space c a n space b e space f o r m e d space s u c h space t h a t space b o t h space c o n s o n a n t s space a n d space v o w e l s space a r e space t o g e t h e r. T h e r e space a r e space 3 space v o w e l s space a n d space 5 space c o n s o n a n t s. T h u s space t h e space t o t a l space n u m b e r space w o r d s space t h a t space c a n space b e space f o r m e d space s o space t h a t space b o t h space c o n s o n a n t s space a n d space v o w e l s space a r e space t o g e t h e r equals 2 cross times 3 factorial cross times 5 factorial equals 1440  3. T h e space r e l a t i v e space p o s i t i o n space o f space t h e space v o w e l s space a n d space t h e space c o n s o n a n t s space u n a l t e r e d space m e a n s comma space v o w e l s space c a n space t a k e space p l a c e space t h e p o s i t i o n space o f space t h e space v o w e l s space a n d space t h e space c o n s o n a n t s space c a n space t a k e space p l a c e space t h e space p o s i t i o n space o f space t h e space c o n s o n a n t s. T h e r e space a r e space 3 space v o w e l s space a n d space 5 space c o n s o n a n t s. T h u s space t h e space t o t a l space n u m b e r space w o r d s space t h a t space c a n space b e space f o r m e d space s o space t h a t space t h e space r e l a t i v e space p o s i t i o n space o f space v o w e l s space a n d space c o n s o n a n t s space u n a l t e r e d space i s equals 3 factorial cross times 5 factorial equals 720
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