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CBSE Class 11-science Answered

Show that the total number of ways in which six '+' and four '-' signs can be arranged in a line such that no two '-' signs occur together is 35.
Asked by shaktidevgun | 26 Sep, 2015, 06:37: PM
answered-by-expert Expert Answer
N u m b e r space o f space apostrophe plus apostrophe space s i g n s equals 6 N u m b e r space o f space apostrophe minus apostrophe space s i g n s equals 4 W e space n e e d space t o space a r r a n g e space t h e space apostrophe minus apostrophe space s i g n s space i n space s u c h space a space w a y space t h a t space n o space t w o space apostrophe minus apostrophe space o c c u r space t o g e t h e r. C o n s i d e r space t h e space f o l l o w i n g space a r r a n g e m e n t colon minus space plus space minus space plus space minus space plus space minus space plus space minus space plus space minus T h u s comma space t h e r e space a r e space 7 space p l a c e s space f o r space apostrophe minus apostrophe space s i g n. W e space n e e d space t o space s e l e c t space 4 space s i g n s space o u t space o f space 7 space p l a c e s space i n space C presuperscript 7 subscript 4 space w a y s. T h u s 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 equals C presuperscript 7 subscript 4 equals fraction numerator 7 factorial over denominator 4 factorial cross times 3 factorial end fraction equals fraction numerator 7 cross times 6 cross times 5 cross times 4 over denominator 1 cross times 2 cross times 3 cross times 4 end fraction equals 35 space w a y s
Answered by Vimala Ramamurthy | 27 Sep, 2015, 08:08: AM

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CBSE 11-science - Maths
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